Work and Wages — Extra Practice

Competitive Mathematics · Time, Work and Distance

6 Part14 worked examples207 practice questions

NoteThis is the Extra Practice set: lots of questions. To learn the methods first, read the main chapter of the same topic (the one without “Extra Practice” in its name), then practise here.

Two masons build a wall together. One could build it alone in 10 days, the other in 15. Would it be fair if the contractor split the total wage equally? No — the first has done more of the work. Wages are always shared in the ratio of the work done. When both work together for the same number of days, the work done by each is decided by his one-day work. The fractions of the work-and-time chapter come back here — only at the end you turn them into rupees.

∑ Formula

मज़दूरी \propto किया गया काम, कुल मज़दूरी = दैनिक मज़दूरी \times दिन

The two basic rules

Sharing the wages

In the ratio of work

The ratio and the share among two and three workers.

Working together: ratios and shares

Fewer days, more pay

The faster worker earns more; the wage ratio is the inverse of the days.

∑ Formula

A : B = \frac{1}{x} : \frac{1}{y} = y : x, तीन में yz : x z : x y

When

x, y

(and

z

) are the days alone

Write each worker’s one-day work $\frac{1}{days}$ .
Form their ratio. To avoid fractions multiply by the LCM of the days — you get a whole-number ratio.
Divide the total wage by the sum of the ratio parts and multiply by each worker’s part.
Check: the shares add up to the total wage.

Example 1 · Basic

A can do a job in 8 days and B in 12 days. They did it together and got ₹1,000. Find their shares.

Solution, step by step

1Ratio $= \frac{1}{8} : \frac{1}{12}$ ; multiplying by the LCM $24$ : $3 : 2$ .
2Total parts $5$ ; A $= 1000 \times \frac{3}{5} = 600$ , B $= 400$

Answer A ₹600, B ₹400

Example 2 · Standard

A, B and C alone take 10, 12 and 15 days. Together they earned ₹3,000. What does each get?

Solution, step by step

1LCM $= 60$ ; ratio $= 6 : 5 : 4$ (sum $15$ ).
2A $= 3000 \times \frac{6}{15} = 1200$ , B $= 1000$ , C $= 800$

Answer A ₹1,200, B ₹1,000, C ₹800

Example 3 · Standard

The first person can do a job in 20 days and the second in 30. Working together, by what percent is the first person’s wage more than the second’s?

Solution, step by step

1Ratio first : second $= 30 : 20 = 3 : 2$ .
2More by $\frac{3 - 2}{2} \times 100 = 50%$ (the base is the one being compared with — the second)

Answer 50%

Example 4 · Standard

A sum can pay A for 30 days or B for 45 days. For how many days can it pay both together?

Solution, step by step

1Money $= 1$ ; daily cost $\frac{1}{30} + \frac{1}{45} = \frac{3 + 2}{90} = \frac{1}{18}$ .
2So $18$ days

Answer 18 days

BasicTry it yourself first

A alone can do a job in 6 days and B in 9 days. If they work together, what is the ratio of their wages (A : B)?

StandardTry it yourself first

A alone can do a job in 14 days and B in 21 days. If they work together, what is the ratio of their wages (A : B)?

AdvancedTry it yourself first

A alone can do a job in 18 days and B in 27 days. If they work together, what is the ratio of their wages (A : B)?

BasicTry it yourself first

A alone can do a job in 4 days and B in 6 days. They worked together and were paid ₹500 in all. What is A's share?

StandardTry it yourself first

A alone can do a job in 12 days and B in 18 days. They worked together and were paid ₹1,000 in all. What is B's share?

StandardTry it yourself first

A alone can do a job in 8 days and B in 12 days. They worked together and were paid ₹1,500 in all. What is A's share?

AdvancedTry it yourself first

A alone can do a job in 15 days and B in 10 days. They worked together and were paid ₹1,200 in all. What is A's share?

AdvancedTry it yourself first

A alone can do a job in 18 days and B in 12 days. They worked together and were paid ₹1,500 in all. What is B's share?

BasicTry it yourself first

A, B and C alone do a job in 6, 12 and 4 days. They did it together and got ₹1,200. What is C's share?

StandardTry it yourself first

A, B and C alone do a job in 10, 15 and 30 days. They did it together and got ₹1,800. What is A's share?

StandardTry it yourself first

A, B and C alone do a job in 8, 12 and 24 days. They did it together and got ₹1,200. What is B's share?

AdvancedTry it yourself first

A, B and C alone do a job in 12, 15 and 20 days. They did it together and got ₹2,400. What is C's share?

AdvancedTry it yourself first

A, B and C alone do a job in 10, 20 and 25 days. They did it together and got ₹3,800. What is A's share?

BasicTry it yourself first

The first person can do a job in 20 days and the second in 25 days. Working together, by what percent is the first person's wage more than the second's?

StandardTry it yourself first

The first person can do a job in 16 days and the second in 24 days. Working together, by what percent is the first person's wage more than the second's?

StandardTry it yourself first

The first person can do a job in 25 days and the second in 40 days. Working together, by what percent is the first person's wage more than the second's?

AdvancedTry it yourself first

The first person can do a job in 20 days and the second in 32 days. Working together, by what percent is the first person's wage more than the second's?

BasicTry it yourself first

A sum of money can pay A for 20 days or B for 30 days. For how many days can it pay both together?

StandardTry it yourself first

A sum of money can pay A for 12 days or B for 24 days. For how many days can it pay both together?

StandardTry it yourself first

A sum of money can pay A for 36 days or B for 45 days. For how many days can it pay both together?

AdvancedTry it yourself first

A sum of money can pay A for 24 days or B for 40 days. For how many days can it pay both together?

Daily wage and days

Rate × days

When every worker has a different daily wage and has worked a different number of days.

Total wages $=$ daily wage $\times$ days. The daily wage comes from it too.
When both the daily-wage ratio and the days worked are given, the share ratio is rate $\times$ days.
A team’s wage $=$ (the team’s one-day earning) $\times$ days, so days $=$ total $\div$ one-day earning.

Example 5 · Standard

The daily wages of A, B and C are in the ratio

4 : 3 : 2

. They worked 5, 6 and 5 days respectively and got ₹2,400 in all. What is A’s share?

Solution, step by step

1Rate $\times$ days: $4 \times 5 = 20$ , $3 \times 6 = 18$ , $2 \times 5 = 10$ (sum $48$ ).
2A $= 2400 \times \frac{20}{48} = 1000$ (B ₹900, C ₹500)

Answer ₹1,000

BasicTry it yourself first

A, B and C did a job for a total wage of ₹3,900. A worked 5 days, B 6 days and C 3 days, and their daily wages are in the ratio 3 : 2 : 4. How much does A get?

StandardTry it yourself first

A, B and C did a job for a total wage of ₹2,200. A worked 6 days, B 4 days and C 4 days, and their daily wages are in the ratio 2 : 3 : 5. How much does C get?

StandardTry it yourself first

A, B and C did a job for a total wage of ₹3,100. A worked 3 days, B 4 days and C 5 days, and their daily wages are in the ratio 4 : 5 : 6. How much does B get?

AdvancedTry it yourself first

A, B and C did a job for a total wage of ₹4,700. A worked 2 days, B 3 days and C 5 days, and their daily wages are in the ratio 6 : 5 : 4. How much does C get?

AdvancedTry it yourself first

A, B and C did a job for a total wage of ₹2,800. A worked 5 days, B 4 days and C 3 days, and their daily wages are in the ratio 3 : 5 : 7. How much does C get?

BasicTry it yourself first

A craftsman gets ₹7,500 for a 30-day month. How much does he earn for working 24 days?

BasicTry it yourself first

A craftsman gets ₹9,000 for a 30-day month. How much does he earn for working 26 days?

StandardTry it yourself first

A craftsman gets ₹8,400 for a 28-day month. How much does he earn for working 24 days?

StandardTry it yourself first

A craftsman gets ₹10,500 for a 30-day month. How much does he earn for working 22 days?

AdvancedTry it yourself first

A craftsman gets ₹14,400 for a 30-day month. How much does he earn for working 27 days?

BasicTry it yourself first

A man gets ₹300 a day and a woman ₹200 a day. A team of 4 men and 5 women was paid ₹13,200. For how many days did the team work?

StandardTry it yourself first

A man gets ₹450 a day and a woman ₹350 a day. A team of 6 men and 8 women was paid ₹27,500. For how many days did the team work?

AdvancedTry it yourself first

A man gets ₹520 a day and a woman ₹380 a day. A team of 7 men and 9 women was paid ₹84,720. For how many days did the team work?

Helpers, leftover work and alternate days

Find each person’s part

A helper joins, someone leaves, leftover work and workers taking turns.

Helpers and leftover work

The whole job

= 1

The unknown person’s part = $1$ minus everyone else’s parts.

Find every worker’s part of the work: $part = days worked \times \frac{1}{days alone}$ .
The unknown worker’s part $= 1 -$ (all the other parts).
Wage $=$ total wage $\times$ part.
Check: the parts add up to $1$ .

Example 6 · Basic

A alone does a job in 24 days but with B’s help in 15 days. The job pays ₹1,600. What does B get?

Solution, step by step

1A’s work in 15 days $= \frac{15}{24} = \frac{5}{8}$ ; B’s $= 1 - \frac{5}{8} = \frac{3}{8}$ .
2B $= 1600 \times \frac{3}{8} = 600$

Answer ₹600

Example 7 · Standard

X alone can do a job in 10 days and Y in 15. With a helper they finished it in 5 days and earned ₹1,800. What does the helper get?

Solution, step by step

1X’s part $= \frac{5}{10} = \frac{1}{2}$ , Y’s $= \frac{5}{15} = \frac{1}{3}$ ; the helper’s $= 1 - \frac{1}{2} - \frac{1}{3} = \frac{1}{6}$ .
2Helper $= 1800 \times \frac{1}{6} = 300$

Answer ₹300

Example 8 · Standard

P, Q and R took a contract for ₹2,400. P and Q did

\frac{5}{12}

of the work and R did the rest. What does R get?

Solution, step by step

1R’s part $= 1 - \frac{5}{12} = \frac{7}{12}$ .
2R $= 2400 \times \frac{7}{12} = 1400$

Answer ₹1,400

Example 9 · Advanced

A can do a job in 12 days and B in 24. They work together for 4 days and M finishes the rest. If the whole job pays ₹1,000, what does M get?

Solution, step by step

1In 4 days $4 (\frac{1}{12} + \frac{1}{24}) = 4 \times \frac{1}{8} = \frac{1}{2}$ is done; the other $\frac{1}{2}$ is M’s.
2M $= 1000 \times \frac{1}{2} = 500$

Answer ₹500

BasicTry it yourself first

A alone does a job in 18 days, but with B's help he finishes it in 10 days. The job pays ₹900. What is B's share?

StandardTry it yourself first

A alone does a job in 30 days, but with B's help he finishes it in 18 days. The job pays ₹1,000. What is B's share?

StandardTry it yourself first

A alone does a job in 24 days, but with B's help he finishes it in 16 days. The job pays ₹900. What is B's share?

AdvancedTry it yourself first

A alone does a job in 40 days, but with B's help he finishes it in 25 days. The job pays ₹1,600. What is B's share?

AdvancedTry it yourself first

A alone does a job in 50 days, but with B's help he finishes it in 30 days. The job pays ₹2,500. What is B's share?

BasicTry it yourself first

X alone can do a job in 12 days and Y in 24 days. With a helper they finished it in 6 days and were paid ₹1,600. What does the helper get?

StandardTry it yourself first

X alone can do a job in 15 days and Y in 20 days. With a helper they finished it in 6 days and were paid ₹1,000. What does the helper get?

StandardTry it yourself first

X alone can do a job in 18 days and Y in 24 days. With a helper they finished it in 8 days and were paid ₹900. What does the helper get?

AdvancedTry it yourself first

X alone can do a job in 16 days and Y in 24 days. With a helper they finished it in 6 days and were paid ₹1,600. What does the helper get?

AdvancedTry it yourself first

X alone can do a job in 20 days and Y in 25 days. With a helper they finished it in 8 days and were paid ₹2,500. What does the helper get?

BasicTry it yourself first

P, Q and R took a contract for ₹1,600. P and Q together did

\frac{3}{8}

of the work and R alone did the rest. How much does R get?

StandardTry it yourself first

P, Q and R took a contract for ₹2,400. P and Q together did

\frac{5}{12}

of the work and R alone did the rest. How much does R get?

StandardTry it yourself first

P, Q and R took a contract for ₹1,500. P and Q together did

\frac{7}{15}

of the work and R alone did the rest. How much does R get?

AdvancedTry it yourself first

P, Q and R took a contract for ₹4,000. P and Q together did

\frac{9}{20}

of the work and R alone did the rest. How much does R get?

BasicTry it yourself first

A can do a job in 12 days and B in 24 days. They work together for 4 days and M finishes the rest. If the whole job pays ₹1,000, how much does M get?

StandardTry it yourself first

A can do a job in 20 days and B in 30 days. They work together for 6 days and M finishes the rest. If the whole job pays ₹1,400, how much does M get?

StandardTry it yourself first

A can do a job in 24 days and B in 40 days. They work together for 10 days and M finishes the rest. If the whole job pays ₹2,400, how much does M get?

AdvancedTry it yourself first

A can do a job in 28 days and B in 42 days. They work together for 12 days and M finishes the rest. If the whole job pays ₹2,100, how much does M get?

AdvancedTry it yourself first

A can do a job in 36 days and B in 45 days. They work together for 10 days and M finishes the rest. If the whole job pays ₹1,600, how much does M get?

Working on alternate days

In proportion to the work actually done

Count the part of the work each person actually did when they took turns.

In alternate-day work the two may not work equal numbers of days (the first can have one day more) and their speeds differ. So pay each one in proportion to the work actually done: walk day by day and count who did how much.

Example 10 · Standard

A can do a job in 10 days and B in 15. They work alternately a day each, A first. If the job pays ₹2,000, what is A’s share?

Solution, step by step

1One cycle does $\frac{1}{10} + \frac{1}{15} = \frac{1}{6}$ ; 6 cycles = 12 days finish it. A worked 6 days: $\frac{6}{10} = \frac{3}{5}$ ; B worked 6 days: $\frac{6}{15} = \frac{2}{5}$ .
2A $= 2000 \times \frac{3}{5} = 1200$ , B $= 800$

Answer A ₹1,200, B ₹800

BasicTry it yourself first

A can do a job in 6 days and B in 12 days. They work on alternate days, A first, and the job pays ₹2,400. What is A's share?

BasicTry it yourself first

A can do a job in 9 days and B in 15 days. They work on alternate days, A first, and the job pays ₹1,800. What is A's share?

StandardTry it yourself first

A can do a job in 10 days and B in 20 days. They work on alternate days, A first, and the job pays ₹2,000. What is A's share?

StandardTry it yourself first

A can do a job in 12 days and B in 24 days. They work on alternate days, A first, and the job pays ₹2,700. What is A's share?

StandardTry it yourself first

A can do a job in 8 days and B in 20 days. They work on alternate days, A first, and the job pays ₹2,000. What is A's share?

AdvancedTry it yourself first

A can do a job in 12 days and B in 18 days. They work on alternate days, A first, and the job pays ₹3,600. What is A's share?

AdvancedTry it yourself first

A can do a job in 14 days and B in 21 days. They work on alternate days, A first, and the job pays ₹2,100. What is A's share?

AdvancedTry it yourself first

A can do a job in 18 days and B in 27 days. They work on alternate days, A first, and the job pays ₹5,400. What is A's share?

Daily rates, fines and groups

Get the rate first, then work it out

Fines for absence, men-women-boys rates and comparing several groups.

Fines and headcount

Account for each day

Splitting the pay across working and absent days; how many people are needed.

∑ Formula

अनुपस्थित दिन = \frac{p N - मिला}{p + f}

N

days, ₹

p

per day worked and a fine of ₹

f

per absent day

Each absent day loses him two things: the day’s pay ₹ $p$ and the fine ₹ $f$ on top. So divide the gap between what he would have earned by attending every day and what he actually got by $(p + f)$ .

Example 11 · Standard

A labourer is hired for 30 days: ₹50 per day worked and a fine of ₹20 per absent day. He got ₹1,080 at the end. How many days was he absent?

Solution, step by step

1Attending every day he would get $30 \times 50 = 1500$ ; shortfall $= 1500 - 1080 = 420$ .
2Loss per absent day $= 50 + 20 = 70$ ⟹ $\frac{420}{70} = 6$ days

Answer 6 days

Example 12 · Standard

15 women got ₹30,000 for 20 days. A man’s daily wage is 1.5 times a woman’s. How many men must work 12 days to earn ₹27,000?

Solution, step by step

1A woman’s daily wage $= \frac{30000}{15 \times 20} = 100$ ; a man’s $= 150$ .
2Men $= \frac{27000}{150 \times 12} = 15$

Answer 15 men

BasicTry it yourself first

A worker is hired for 40 days: ₹15 for each day worked and a fine of ₹5 for each day absent. At the end he received ₹480. For how many days was he absent?

BasicTry it yourself first

A worker is hired for 30 days: ₹20 for each day worked and a fine of ₹8 for each day absent. At the end he received ₹488. For how many days was he absent?

StandardTry it yourself first

A worker is hired for 60 days: ₹25 for each day worked and a fine of ₹10 for each day absent. At the end he received ₹1,220. For how many days was he absent?

StandardTry it yourself first

A worker is hired for 45 days: ₹18 for each day worked and a fine of ₹6 for each day absent. At the end he received ₹690. For how many days was he absent?

AdvancedTry it yourself first

A worker is hired for 50 days: ₹40 for each day worked and a fine of ₹15 for each day absent. At the end he received ₹1,450. For how many days was he absent?

AdvancedTry it yourself first

A worker is hired for 90 days: ₹30 for each day worked and a fine of ₹10 for each day absent. At the end he received ₹2,100. For how many days was he absent?

BasicTry it yourself first

12 women earned ₹7,200 in all for 15 days. A man's daily wage is 2 times a woman's. How many men must work 10 days to earn ₹14,400?

StandardTry it yourself first

20 women earned ₹12,000 in all for 12 days. A man's daily wage is 3 times a woman's. How many men must work 8 days to earn ₹36,000?

StandardTry it yourself first

16 women earned ₹12,960 in all for 18 days. A man's daily wage is 2 times a woman's. How many men must work 12 days to earn ₹25,920?

AdvancedTry it yourself first

25 women earned ₹36,000 in all for 24 days. A man's daily wage is 2 times a woman's. How many men must work 15 days to earn ₹72,000?

Men, women and boys

Convert to one unit

Rate relations and finding one group’s wage from another’s.

Take the daily wage of the lowest-paid (often the boy) as $x$ .
Write the other rates in terms of $x$ using the relations (“ $p$ men $= q$ women”).
Find $x$ from the first group’s total, then compute the second group.
When totals of several pairs are given, find the daily sums and add or subtract them.

Example 13 · Standard

2 men earn as much as 3 women, and 3 women as much as 4 boys. 6 men, 6 women and 3 boys together earn ₹2,300. What is a man’s daily wage?

Solution, step by step

1Boy $= b$ ⟹ 3 women $= 4 b$ , one woman $= \frac{4 b}{3}$ ; 2 men $= 4 b$ , one man $= 2 b$ .
2 $6 (2 b) + 6 (\frac{4 b}{3}) + 3 b = 12 b + 8 b + 3 b = 23 b = 2300$ ⟹ $b = 100$ ; man $= 200$

Answer ₹200

BasicTry it yourself first

A, B and C together were paid ₹1,080 for 12 days. A and C together were paid ₹750 for 15 days, and B and C together ₹600 for 10 days, at the same daily rates. What is C's daily wage?

StandardTry it yourself first

A, B and C together were paid ₹1,100 for 10 days. A and C together were paid ₹1,350 for 18 days, and B and C together ₹1,200 for 20 days, at the same daily rates. What is C's daily wage?

StandardTry it yourself first

A, B and C together were paid ₹1,890 for 14 days. A and C together were paid ₹1,200 for 16 days, and B and C together ₹1,080 for 12 days, at the same daily rates. What is C's daily wage?

AdvancedTry it yourself first

A, B and C together were paid ₹3,500 for 20 days. A and C together were paid ₹2,880 for 24 days, and B and C together ₹2,850 for 30 days, at the same daily rates. What is C's daily wage?

AdvancedTry it yourself first

A, B and C together were paid ₹3,240 for 18 days. A and C together were paid ₹2,420 for 22 days, and B and C together ₹1,725 for 15 days, at the same daily rates. What is C's daily wage?

BasicTry it yourself first

The wages of 2 men equal those of 3 women, and 3 women equal 4 boys. If 3 men, 4 women and 2 boys earn ₹120 in all, what do 5 men, 2 women and 3 boys earn?

StandardTry it yourself first

The wages of 3 men equal those of 5 women, and 2 women equal 3 boys. If 4 men, 3 women and 5 boys earn ₹117 in all, what do 6 men, 2 women and 3 boys earn?

StandardTry it yourself first

The wages of 4 men equal those of 6 women, and 3 women equal 5 boys. If 2 men, 3 women and 4 boys earn ₹84 in all, what do 5 men, 4 women and 2 boys earn?

AdvancedTry it yourself first

The wages of 5 men equal those of 6 women, and 4 women equal 5 boys. If 5 men, 4 women and 6 boys earn ₹148 in all, what do 7 men, 6 women and 5 boys earn?

AdvancedTry it yourself first

The wages of 3 men equal those of 2 women, and 5 women equal 6 boys. If 6 men, 5 women and 4 boys earn ₹148 in all, what do 9 men, 8 women and 7 boys earn?

BasicTry it yourself first

Men, women and children are employed in the ratio 4 : 3 : 2 with wages in the ratio 6 : 4 : 3. When 80 men are employed, the total daily wages are ₹4,200. What is a man's daily wage?

StandardTry it yourself first

Men, women and children are employed in the ratio 5 : 3 : 2 with wages in the ratio 8 : 5 : 3. When 100 men are employed, the total daily wages are ₹4,880. What is a man's daily wage?

StandardTry it yourself first

Men, women and children are employed in the ratio 3 : 2 : 1 with wages in the ratio 7 : 4 : 3. When 60 men are employed, the total daily wages are ₹3,200. What is a man's daily wage?

AdvancedTry it yourself first

Men, women and children are employed in the ratio 6 : 4 : 3 with wages in the ratio 9 : 6 : 4. When 120 men are employed, the total daily wages are ₹5,400. What is a man's daily wage?

Traps and fast tricks

Slips · tricks

Where marks go in wage questions.

The commonest mistakes

Six traps

The slips that cost marks.

Trap 1Taking the ratio of days as the ratio of wages. The one who takes fewer days earns more — the ratio is flipped.

Trap 2Splitting the total equally. Equal only when their one-day works are equal.

Trap 3Forgetting the whole job is $1$ while finding the helper’s part. Helper’s part

= 1 -

everyone else’s parts.

Trap 4Subtracting only the fine. The absent day’s pay is lost too — divide by

p + f

Trap 5Using the wrong base for “percent more”. Divide by the one you are comparing with (the second).

Trap 6Assuming equal days in alternate work. The first can work one extra day; count the real work done.

Fast tricks

LCM ratio and checks

Habits for speed.

LCM ratio: take the LCM of the days; $\frac{LCM}{days}$ is each person’s part.
Two persons: workers taking $x$ and $y$ days earn $y : x$ — split the total into $(x + y)$ parts.
Helper questions: write each person’s work in the given days as a fraction; the leftover is the helper’s.
Check: shares add to the total; whoever did more work gets more.
Test the options: the shares must sum to the total — this alone rejects many options.

Example 14 · Standard

A, B and C earned ₹3,600 for a job. A and B together did

\frac{7}{12}

of it and C the rest. What is C’s share?

Solution, step by step

1C’s part $= 1 - \frac{7}{12} = \frac{5}{12}$ .
2C $= 3600 \times \frac{5}{12} = 1500$

Answer ₹1,500

The practice ladder

Basic → standard → advanced

New questions of every type, in three levels.

Level 1 — Basic

Direct rules

One-rule questions.

BasicTry it yourself first

A alone can do a job in 4 days and B in 6 days. If they work together, what is the ratio of their wages (A : B)?

BasicTry it yourself first

A alone can do a job in 10 days and B in 15 days. If they work together, what is the ratio of their wages (A : B)?

BasicTry it yourself first

A alone can do a job in 8 days and B in 12 days. If they work together, what is the ratio of their wages (A : B)?

BasicTry it yourself first

A alone can do a job in 10 days and B in 15 days. They worked together and were paid ₹750 in all. What is A's share?

BasicTry it yourself first

A alone can do a job in 6 days and B in 9 days. They worked together and were paid ₹1,500 in all. What is B's share?

BasicTry it yourself first

A alone can do a job in 9 days and B in 18 days. They worked together and were paid ₹2,400 in all. What is B's share?

BasicTry it yourself first

A alone can do a job in 20 days and B in 30 days. They worked together and were paid ₹1,000 in all. What is A's share?

BasicTry it yourself first

A, B and C alone do a job in 9, 18 and 6 days. They did it together and got ₹1,800. What is C's share?

BasicTry it yourself first

A, B and C alone do a job in 5, 10 and 20 days. They did it together and got ₹2,800. What is A's share?

BasicTry it yourself first

A, B and C alone do a job in 16, 24 and 48 days. They did it together and got ₹3,000. What is B's share?

BasicTry it yourself first

A alone does a job in 15 days, but with B's help he finishes it in 9 days. The job pays ₹750. What is B's share?

BasicTry it yourself first

A alone does a job in 12 days, but with B's help he finishes it in 8 days. The job pays ₹900. What is B's share?

BasicTry it yourself first

X alone can do a job in 14 days and Y in 28 days. With a helper they finished it in 7 days and were paid ₹1,200. What does the helper get?

BasicTry it yourself first

X alone can do a job in 8 days and Y in 12 days. With a helper they finished it in 4 days and were paid ₹900. What does the helper get?

BasicTry it yourself first

P, Q and R took a contract for ₹1,800. P and Q together did

\frac{2}{9}

of the work and R alone did the rest. How much does R get?

BasicTry it yourself first

P, Q and R took a contract for ₹2,000. P and Q together did

\frac{3}{10}

of the work and R alone did the rest. How much does R get?

BasicTry it yourself first

A can do a job in 10 days and B in 15 days. They work together for 3 days and M finishes the rest. If the whole job pays ₹900, how much does M get?

BasicTry it yourself first

A can do a job in 30 days and B in 45 days. They work together for 9 days and M finishes the rest. If the whole job pays ₹1,800, how much does M get?

BasicTry it yourself first

A, B and C did a job for a total wage of ₹2,800. A worked 9 days, B 6 days and C 5 days, and their daily wages are in the ratio 2 : 3 : 4. How much does C get?

BasicTry it yourself first

A, B and C did a job for a total wage of ₹2,900. A worked 4 days, B 5 days and C 6 days, and their daily wages are in the ratio 5 : 4 : 3. How much does A get?

BasicTry it yourself first

A worker is hired for 25 days: ₹30 for each day worked and a fine of ₹10 for each day absent. At the end he received ₹630. For how many days was he absent?

BasicTry it yourself first

A worker is hired for 20 days: ₹50 for each day worked and a fine of ₹20 for each day absent. At the end he received ₹860. For how many days was he absent?

BasicTry it yourself first

A craftsman gets ₹6,600 for a 22-day month. How much does he earn for working 18 days?

BasicTry it yourself first

A craftsman gets ₹5,400 for a 27-day month. How much does he earn for working 25 days?

BasicTry it yourself first

The first person can do a job in 8 days and the second in 10 days. Working together, by what percent is the first person's wage more than the second's?

BasicTry it yourself first

The first person can do a job in 24 days and the second in 30 days. Working together, by what percent is the first person's wage more than the second's?

BasicTry it yourself first

A sum of money can pay A for 12 days or B for 36 days. For how many days can it pay both together?

BasicTry it yourself first

A sum of money can pay A for 10 days or B for 15 days. For how many days can it pay both together?

BasicTry it yourself first

A man gets ₹250 a day and a woman ₹150 a day. A team of 3 men and 4 women was paid ₹9,450. For how many days did the team work?

BasicTry it yourself first

A man gets ₹400 a day and a woman ₹300 a day. A team of 5 men and 5 women was paid ₹14,000. For how many days did the team work?

BasicTry it yourself first

A can do a job in 6 days and B in 12 days. They work on alternate days, A first, and the job pays ₹1,800. What is A's share?

BasicTry it yourself first

10 women earned ₹3,600 in all for 12 days. A man's daily wage is 2 times a woman's. How many men must work 6 days to earn ₹9,000?

Level 2 — Standard

Two ideas combined

Exam-level questions.

StandardTry it yourself first

A alone can do a job in 12 days and B in 18 days. If they work together, what is the ratio of their wages (A : B)?

StandardTry it yourself first

A alone can do a job in 16 days and B in 20 days. If they work together, what is the ratio of their wages (A : B)?

StandardTry it yourself first

A alone can do a job in 9 days and B in 15 days. If they work together, what is the ratio of their wages (A : B)?

StandardTry it yourself first

A alone can do a job in 7 days and B in 14 days. They worked together and were paid ₹2,100 in all. What is B's share?

StandardTry it yourself first

A alone can do a job in 24 days and B in 36 days. They worked together and were paid ₹1,800 in all. What is A's share?

StandardTry it yourself first

A alone can do a job in 30 days and B in 45 days. They worked together and were paid ₹1,500 in all. What is A's share?

StandardTry it yourself first

A alone can do a job in 10 days and B in 40 days. They worked together and were paid ₹1,000 in all. What is B's share?

StandardTry it yourself first

A alone can do a job in 12 days and B in 16 days. They worked together and were paid ₹2,100 in all. What is A's share?

StandardTry it yourself first

A, B and C alone do a job in 12, 18 and 36 days. They did it together and got ₹3,600. What is B's share?

StandardTry it yourself first

A, B and C alone do a job in 14, 21 and 42 days. They did it together and got ₹2,400. What is C's share?

StandardTry it yourself first

A, B and C alone do a job in 15, 20 and 30 days. They did it together and got ₹2,700. What is A's share?

StandardTry it yourself first

A, B and C alone do a job in 18, 24 and 36 days. They did it together and got ₹4,500. What is C's share?

StandardTry it yourself first

A alone does a job in 36 days, but with B's help he finishes it in 24 days. The job pays ₹1,200. What is B's share?

StandardTry it yourself first

A alone does a job in 45 days, but with B's help he finishes it in 30 days. The job pays ₹1,800. What is B's share?

StandardTry it yourself first

X alone can do a job in 30 days and Y in 40 days. With a helper they finished it in 12 days and were paid ₹2,000. What does the helper get?

StandardTry it yourself first

X alone can do a job in 36 days and Y in 45 days. With a helper they finished it in 15 days and were paid ₹2,400. What does the helper get?

StandardTry it yourself first

X alone can do a job in 14 days and Y in 28 days. With a helper they finished it in 7 days and were paid ₹1,200. What does the helper get?

StandardTry it yourself first

P, Q and R took a contract for ₹1,200. P and Q together did

\frac{1}{6}

of the work and R alone did the rest. How much does R get?

StandardTry it yourself first

P, Q and R took a contract for ₹2,200. P and Q together did

\frac{4}{11}

of the work and R alone did the rest. How much does R get?

StandardTry it yourself first

A can do a job in 16 days and B in 48 days. They work together for 6 days and M finishes the rest. If the whole job pays ₹1,600, how much does M get?

StandardTry it yourself first

A can do a job in 30 days and B in 45 days. They work together for 9 days and M finishes the rest. If the whole job pays ₹1,800, how much does M get?

StandardTry it yourself first

A can do a job in 20 days and B in 60 days. They work together for 10 days and M finishes the rest. If the whole job pays ₹1,500, how much does M get?

StandardTry it yourself first

A, B and C did a job for a total wage of ₹3,200. A worked 5 days, B 8 days and C 10 days, and their daily wages are in the ratio 4 : 3 : 2. How much does B get?

StandardTry it yourself first

A, B and C did a job for a total wage of ₹2,800. A worked 9 days, B 6 days and C 5 days, and their daily wages are in the ratio 2 : 3 : 4. How much does A get?

StandardTry it yourself first

A, B and C did a job for a total wage of ₹4,200. A worked 3 days, B 5 days and C 6 days, and their daily wages are in the ratio 8 : 6 : 5. How much does B get?

StandardTry it yourself first

A worker is hired for 36 days: ₹24 for each day worked and a fine of ₹9 for each day absent. At the end he received ₹666. For how many days was he absent?

StandardTry it yourself first

A worker is hired for 28 days: ₹35 for each day worked and a fine of ₹12 for each day absent. At the end he received ₹792. For how many days was he absent?

StandardTry it yourself first

A worker is hired for 24 days: ₹40 for each day worked and a fine of ₹15 for each day absent. At the end he received ₹685. For how many days was he absent?

StandardTry it yourself first

A craftsman gets ₹12,000 for a 25-day month. How much does he earn for working 20 days?

StandardTry it yourself first

A craftsman gets ₹16,500 for a 30-day month. How much does he earn for working 28 days?

StandardTry it yourself first

The first person can do a job in 15 days and the second in 18 days. Working together, by what percent is the first person's wage more than the second's?

StandardTry it yourself first

The first person can do a job in 40 days and the second in 48 days. Working together, by what percent is the first person's wage more than the second's?

StandardTry it yourself first

The first person can do a job in 12 days and the second in 18 days. Working together, by what percent is the first person's wage more than the second's?

StandardTry it yourself first

A sum of money can pay A for 16 days or B for 48 days. For how many days can it pay both together?

StandardTry it yourself first

A sum of money can pay A for 60 days or B for 40 days. For how many days can it pay both together?

StandardTry it yourself first

A sum of money can pay A for 14 days or B for 35 days. For how many days can it pay both together?

StandardTry it yourself first

A can do a job in 10 days and B in 15 days. They work on alternate days, A first, and the job pays ₹3,600. What is A's share?

StandardTry it yourself first

A can do a job in 15 days and B in 30 days. They work on alternate days, A first, and the job pays ₹1,500. What is A's share?

StandardTry it yourself first

A can do a job in 8 days and B in 16 days. They work on alternate days, A first, and the job pays ₹3,200. What is A's share?

StandardTry it yourself first

18 women earned ₹19,800 in all for 20 days. A man's daily wage is 2 times a woman's. How many men must work 10 days to earn ₹39,600?

StandardTry it yourself first

14 women earned ₹16,800 in all for 25 days. A man's daily wage is 3 times a woman's. How many men must work 14 days to earn ₹40,320?

StandardTry it yourself first

A man gets ₹500 a day and a woman ₹320 a day. A team of 8 men and 10 women was paid ₹64,800. For how many days did the team work?

StandardTry it yourself first

A, B and C together were paid ₹1,300 for 10 days. A and C together were paid ₹900 for 12 days, and B and C together ₹1,440 for 16 days, at the same daily rates. What is C's daily wage?

StandardTry it yourself first

The wages of 2 men equal those of 3 women, and 3 women equal 4 boys. If 5 men, 2 women and 3 boys earn ₹188 in all, what do 4 men, 6 women and 8 boys earn?

StandardTry it yourself first

Men, women and children are employed in the ratio 4 : 3 : 2 with wages in the ratio 7 : 5 : 3. When 40 men are employed, the total daily wages are ₹2,940. What is a man's daily wage?

Level 3 — Advanced

Many steps and clever thinking

Questions at the hard end of competitive exams.

AdvancedTry it yourself first

A alone can do a job in 24 days and B in 36 days. If they work together, what is the ratio of their wages (A : B)?

AdvancedTry it yourself first

A alone can do a job in 35 days and B in 42 days. If they work together, what is the ratio of their wages (A : B)?

AdvancedTry it yourself first

A alone can do a job in 28 days and B in 45 days. If they work together, what is the ratio of their wages (A : B)?

AdvancedTry it yourself first

A alone can do a job in 24 days and B in 40 days. They worked together and were paid ₹4,000 in all. What is B's share?

AdvancedTry it yourself first

A alone can do a job in 15 days and B in 35 days. They worked together and were paid ₹2,000 in all. What is B's share?

AdvancedTry it yourself first

A alone can do a job in 18 days and B in 30 days. They worked together and were paid ₹4,800 in all. What is A's share?

AdvancedTry it yourself first

A alone can do a job in 36 days and B in 45 days. They worked together and were paid ₹1,800 in all. What is A's share?

AdvancedTry it yourself first

A, B and C alone do a job in 25, 30 and 50 days. They did it together and got ₹2,800. What is B's share?

AdvancedTry it yourself first

A, B and C alone do a job in 8, 10 and 20 days. They did it together and got ₹3,300. What is C's share?

AdvancedTry it yourself first

A, B and C alone do a job in 10, 20 and 25 days. They did it together and got ₹3,800. What is B's share?

AdvancedTry it yourself first

A, B and C alone do a job in 12, 20 and 15 days. They did it together and got ₹2,400. What is A's share?

AdvancedTry it yourself first

A alone does a job in 60 days, but with B's help he finishes it in 40 days. The job pays ₹3,000. What is B's share?

AdvancedTry it yourself first

A alone does a job in 48 days, but with B's help he finishes it in 32 days. The job pays ₹1,800. What is B's share?

AdvancedTry it yourself first

X alone can do a job in 18 days and Y in 24 days. With a helper they finished it in 8 days and were paid ₹900. What does the helper get?

AdvancedTry it yourself first

X alone can do a job in 12 days and Y in 16 days. With a helper they finished it in 6 days and were paid ₹2,000. What does the helper get?

AdvancedTry it yourself first

X alone can do a job in 9 days and Y in 18 days. With a helper they finished it in 4 days and were paid ₹1,500. What does the helper get?

AdvancedTry it yourself first

P, Q and R took a contract for ₹3,200. P and Q together did

\frac{5}{16}

of the work and R alone did the rest. How much does R get?

AdvancedTry it yourself first

P, Q and R took a contract for ₹2,100. P and Q together did

\frac{3}{7}

of the work and R alone did the rest. How much does R get?

AdvancedTry it yourself first

A can do a job in 12 days and B in 20 days. They work together for 5 days and M finishes the rest. If the whole job pays ₹2,400, how much does M get?

AdvancedTry it yourself first

A can do a job in 24 days and B in 40 days. They work together for 10 days and M finishes the rest. If the whole job pays ₹2,400, how much does M get?

AdvancedTry it yourself first

A can do a job in 28 days and B in 42 days. They work together for 12 days and M finishes the rest. If the whole job pays ₹2,100, how much does M get?

AdvancedTry it yourself first

A, B and C did a job for a total wage of ₹4,400. A worked 4 days, B 6 days and C 10 days, and their daily wages are in the ratio 7 : 5 : 3. How much does A get?

AdvancedTry it yourself first

A, B and C did a job for a total wage of ₹5,800. A worked 10 days, B 4 days and C 6 days, and their daily wages are in the ratio 2 : 5 : 3. How much does B get?

AdvancedTry it yourself first

A, B and C did a job for a total wage of ₹4,100. A worked 8 days, B 4 days and C 6 days, and their daily wages are in the ratio 3 : 7 : 5. How much does C get?

AdvancedTry it yourself first

A, B and C did a job for a total wage of ₹3,600. A worked 2 days, B 4 days and C 6 days, and their daily wages are in the ratio 9 : 6 : 5. How much does C get?

AdvancedTry it yourself first

A worker is hired for 75 days: ₹36 for each day worked and a fine of ₹14 for each day absent. At the end he received ₹2,100. For how many days was he absent?

AdvancedTry it yourself first

A worker is hired for 80 days: ₹45 for each day worked and a fine of ₹15 for each day absent. At the end he received ₹2,940. For how many days was he absent?

AdvancedTry it yourself first

A worker is hired for 120 days: ₹25 for each day worked and a fine of ₹10 for each day absent. At the end he received ₹2,300. For how many days was he absent?

AdvancedTry it yourself first

A craftsman gets ₹21,000 for a 30-day month. How much does he earn for working 29 days?

AdvancedTry it yourself first

The first person can do a job in 24 days and the second in 30 days. Working together, by what percent is the first person's wage more than the second's?

AdvancedTry it yourself first

The first person can do a job in 35 days and the second in 49 days. Working together, by what percent is the first person's wage more than the second's?

AdvancedTry it yourself first

The first person can do a job in 30 days and the second in 42 days. Working together, by what percent is the first person's wage more than the second's?

AdvancedTry it yourself first

A sum of money can pay A for 28 days or B for 84 days. For how many days can it pay both together?

AdvancedTry it yourself first

A sum of money can pay A for 24 days or B for 40 days. For how many days can it pay both together?

AdvancedTry it yourself first

A can do a job in 6 days and B in 18 days. They work on alternate days, A first, and the job pays ₹1,800. What is A's share?

AdvancedTry it yourself first

A can do a job in 12 days and B in 18 days. They work on alternate days, A first, and the job pays ₹3,600. What is A's share?

AdvancedTry it yourself first

A can do a job in 18 days and B in 27 days. They work on alternate days, A first, and the job pays ₹5,400. What is A's share?

AdvancedTry it yourself first

A can do a job in 14 days and B in 21 days. They work on alternate days, A first, and the job pays ₹2,100. What is A's share?

AdvancedTry it yourself first

30 women earned ₹42,000 in all for 20 days. A man's daily wage is 2 times a woman's. How many men must work 15 days to earn ₹1,17,600?

AdvancedTry it yourself first

24 women earned ₹36,960 in all for 28 days. A man's daily wage is 3 times a woman's. How many men must work 12 days to earn ₹69,300?

AdvancedTry it yourself first

A man gets ₹640 a day and a woman ₹480 a day. A team of 12 men and 15 women was paid ₹1,63,680. For how many days did the team work?

AdvancedTry it yourself first

A, B and C together were paid ₹5,280 for 24 days. A and C together were paid ₹4,350 for 30 days, and B and C together ₹2,600 for 20 days, at the same daily rates. What is C's daily wage?

AdvancedTry it yourself first

The wages of 4 men equal those of 5 women, and 3 women equal 4 boys. If 6 men, 4 women and 8 boys earn ₹280 in all, what do 10 men, 9 women and 7 boys earn?

AdvancedTry it yourself first

The wages of 5 men equal those of 8 women, and 2 women equal 3 boys. If 5 men, 3 women and 4 boys earn ₹205 in all, what do 8 men, 6 women and 9 boys earn?

AdvancedTry it yourself first

Men, women and children are employed in the ratio 5 : 3 : 2 with wages in the ratio 8 : 6 : 5. When 150 men are employed, the total daily wages are ₹8,160. What is a man's daily wage?

Revision — formula cards

Flip each card and test yourself

Read the front, think, then flip.