Work and Wages

Competitive Mathematics · Time, Work and Distance

6 Part5 worked examples34 practice questions

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.

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.

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.

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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.

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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.

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Men, women and boys

Convert to one unit

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

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Traps and fast tricks

Slips · tricks

Where marks go in wage questions.

The commonest mistakes

Six traps

The slips that cost marks.

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Fast tricks

LCM ratio and checks

Habits for speed.

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The practice ladder

Basic → standard → advanced

New questions of every type, in three levels.

Level 1 — Basic

Direct rules

One-rule questions.

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Level 2 — Standard

Two ideas combined

Exam-level questions.

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Level 3 — Advanced

Many steps and clever thinking

Questions at the hard end of competitive exams.

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Revision — formula cards

Flip each card and test yourself

Read the front, think, then flip.

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Work and Wages

Sharing the wages

Working together: ratios and shares

Daily wage and days

Helpers, leftover work and alternate days

Helpers and leftover work

Working on alternate days

Daily rates, fines and groups

Fines and headcount

Men, women and boys

Traps and fast tricks

The commonest mistakes

Fast tricks

The practice ladder

Level 1 — Basic

Level 2 — Standard

Level 3 — Advanced

Revision — formula cards

Free All Access Passevery mind map · Hindi + English · 12 months

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