Work and Time — Extra Practice

Competitive Mathematics · Time, Work and Distance

7 Part13 worked examples197 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.

A painter takes 10 days to paint a whole wall. How much of the wall does the painter finish in one day? One-tenth. That is the foundation of this chapter: a job done in $n$ days has a one-day work of $\frac{1}{n}$ . When two people work together their one-day works add, when someone leaves they drop, and in the end the work done must equal $1$ (the whole job).

∑ Formula

1 दिन का काम = \frac{1}{n}, काम = दर \times समय

The first formula

Working together

Add the rates, not the days

Finding the time for two or three workers together, and one worker’s time when the pair is known.

Two or three workers together

\frac{1}{a} + \frac{1}{b}

Add each worker’s one-day work to get the time together.

∑ Formula

साथ का समय = \frac{ab}{a + b} (तीन के लिए \frac{1}{\frac{1}{a} + \frac{1}{b} + \frac{1}{c}})

Time taken together

Write each person’s one-day work: $\frac{1}{a}, \frac{1}{b}$ .
Add them — this is the one-day work together.
The reciprocal (the fraction turned upside down) is the time together.
Check: the time together must be less than either worker’s time alone.

Example 1 · Basic

A can do a job in 12 days and B in 4 days. How long will they take together?

Solution, step by step

1One-day work $= \frac{1}{12} + \frac{1}{4} = \frac{1 + 3}{12} = \frac{4}{12} = \frac{1}{3}$ .
2So the time is $3$ days — less than both 4 and 12 ✓

Answer 3 days

Example 2 · Standard

A, B and C alone do a job in 10, 15 and 30 days. How long will all three take together?

Solution, step by step

1 $\frac{1}{10} + \frac{1}{15} + \frac{1}{30} = \frac{3 + 2 + 1}{30} = \frac{6}{30} = \frac{1}{5}$ .
2Time $= 5$ days

Answer 5 days

BasicTry it yourself first

A alone can finish a job in 6 days and B alone in 3 days. In how many days will they finish it working together?

BasicTry it yourself first

A alone can finish a job in 20 days and B alone in 5 days. In how many days will they finish it working together?

StandardTry it yourself first

A alone can finish a job in 9 days and B alone in 18 days. In how many days will they finish it working together?

StandardTry it yourself first

A alone can finish a job in 14 days and B alone in 21 days. In how many days will they finish it working together?

StandardTry it yourself first

A alone can finish a job in 8 days and B alone in 12 days. In how many days will they finish it working together?

AdvancedTry it yourself first

A alone can finish a job in 7 days and B alone in 11 days. In how many days will they finish it working together?

AdvancedTry it yourself first

A alone can finish a job in 16 days and B alone in 24 days. In how many days will they finish it working together?

BasicTry it yourself first

A, B and C can do a job alone in 6, 12 and 12 days. In how many days will they do it together?

StandardTry it yourself first

A, B and C can do a job alone in 12, 18 and 36 days. In how many days will they do it together?

StandardTry it yourself first

A, B and C can do a job alone in 10, 20 and 25 days. In how many days will they do it together?

AdvancedTry it yourself first

A, B and C can do a job alone in 8, 12 and 24 days. In how many days will they do it together?

AdvancedTry it yourself first

A, B and C can do a job alone in 15, 20 and 30 days. In how many days will they do it together?

Pair known, find one worker

Subtract

When the pair’s one-day work and one worker’s are given, find the other’s.

∑ Formula

\frac{1}{b} = \frac{1}{x} - \frac{1}{a} ⟹ b = \frac{a x}{a - x}

The other worker’s time

If the pair takes $x$ days and A takes $a$ days alone, then B’s one-day work = the pair’s work minus A’s. Notice that $a$ is always larger than $x$ — a single worker is always slower than the pair.

Example 3 · Standard

A and B together finish a job in 6 days. A alone takes 15 days. How long does B alone take?

Solution, step by step

1B’s one-day work $= \frac{1}{6} - \frac{1}{15} = \frac{5 - 2}{30} = \frac{1}{10}$ .
2So B alone takes $10$ days.

Answer 10 days

BasicTry it yourself first

A and B together do a job in 4 days. A alone can do it in 12 days. In how many days can B alone do it?

BasicTry it yourself first

A and B together do a job in 6 days. A alone can do it in 10 days. In how many days can B alone do it?

StandardTry it yourself first

A and B together do a job in 12 days. A alone can do it in 20 days. In how many days can B alone do it?

StandardTry it yourself first

A and B together do a job in 8 days. A alone can do it in 24 days. In how many days can B alone do it?

StandardTry it yourself first

A and B together do a job in 15 days. A alone can do it in 40 days. In how many days can B alone do it?

AdvancedTry it yourself first

A and B together do a job in 9 days. A alone can do it in 21 days. In how many days can B alone do it?

AdvancedTry it yourself first

A and B together do a job in 14 days. A alone can do it in 35 days. In how many days can B alone do it?

Efficiency and ratios

Faster worker, fewer days

Efficiency ratios, “ $n$ times as efficient”, “ $p %$ more efficient” and pair questions.

Efficiency and time are inverse

The time ratio flips

A worker $n$ times as fast takes $\frac{1}{n}$ of the time.

Efficiency $\propto \frac{1}{time}$ : a worker twice as fast takes half the time.
If A is $n$ times as efficient as B, the time ratio A : B is $1 : n$ .
“ $p %$ more efficient” means the efficiency ratio is $(100 + p) : 100$ , so the time ratio is $100 : (100 + p)$ .
When told someone takes “ $d$ days less”, make the difference of the time-ratio parts equal to $d$ .

Example 4 · Basic

Ravi works 3 times as fast as Shyam. Together they finish a job in 12 days. How long would Shyam alone take?

Solution, step by step

1Rates: Ravi $3$ , Shyam $1$ unit/day; together $= 4$ units/day.
2Total work $= 4 \times 12 = 48$ units; Shyam alone $= \frac{48}{1} = 48$ days (Ravi 16 days).

Answer 48 days

Example 5 · Standard

Kamal is 25% more efficient than Vimal. Vimal alone takes 20 days. How long does Kamal take?

Solution, step by step

1Efficiency ratio Kamal : Vimal $= 125 : 100 = 5 : 4$ ⟹ time ratio $4 : 5$ .
2Kamal’s time $= 20 \times \frac{4}{5} = 16$ days

Answer 16 days

BasicTry it yourself first

P is 2 times as efficient as Q and takes 6 days less. In how many days can P and Q each do the work alone?

BasicTry it yourself first

P is 3 times as efficient as Q and takes 8 days less. In how many days can P and Q each do the work alone?

StandardTry it yourself first

P is 4 times as efficient as Q and takes 9 days less. In how many days can P and Q each do the work alone?

StandardTry it yourself first

P is 3 times as efficient as Q and takes 14 days less. In how many days can P and Q each do the work alone?

StandardTry it yourself first

P is 5 times as efficient as Q and takes 12 days less. In how many days can P and Q each do the work alone?

AdvancedTry it yourself first

P is 4 times as efficient as Q and takes 15 days less. In how many days can P and Q each do the work alone?

AdvancedTry it yourself first

P is 2 times as efficient as Q and takes 13 days less. In how many days can P and Q each do the work alone?

BasicTry it yourself first

Kamal is 25% more efficient than Vimal. Vimal alone does a job in 20 days. In how many days can Kamal do it alone?

StandardTry it yourself first

Kamal is 50% more efficient than Vimal. Vimal alone does a job in 30 days. In how many days can Kamal do it alone?

StandardTry it yourself first

Kamal is 20% more efficient than Vimal. Vimal alone does a job in 36 days. In how many days can Kamal do it alone?

AdvancedTry it yourself first

Kamal is 60% more efficient than Vimal. Vimal alone does a job in 40 days. In how many days can Kamal do it alone?

AdvancedTry it yourself first

Kamal is 150% more efficient than Vimal. Vimal alone does a job in 50 days. In how many days can Kamal do it alone?

From pairs to singles

Add the three pairs

Given the times of A+B, B+C and C+A, find all three together.

∑ Formula

A + B + C = \frac{1}{2} (\frac{1}{x} + \frac{1}{y} + \frac{1}{z})

From the three pairs

Adding the one-day work of the three pairs counts every person twice, so halving the sum gives the work of all three together. Subtract any pair’s work and you get the third person’s work alone.

Example 6 · Standard

A+B, B+C and C+A finish a job in 12, 15 and 20 days. How long will all three take together?

Solution, step by step

1 $2 (A + B + C) = \frac{1}{12} + \frac{1}{15} + \frac{1}{20} = \frac{5 + 4 + 3}{60} = \frac{12}{60} = \frac{1}{5}$ .
2 $A + B + C = \frac{1}{10}$ ⟹ $10$ days

Answer 10 days

BasicTry it yourself first

A and B do a job in 12 days, B and C in 15 days and C and A in 20 days. How long will all three take together?

BasicTry it yourself first

A and B do a job in 6 days, B and C in 8 days and C and A in 12 days. How long will all three take together?

StandardTry it yourself first

A and B do a job in 10 days, B and C in 15 days and C and A in 24 days. How long will all three take together?

StandardTry it yourself first

A and B do a job in 20 days, B and C in 30 days and C and A in 12 days. How long will all three take together?

AdvancedTry it yourself first

A and B do a job in 18 days, B and C in 24 days and C and A in 36 days. How long will all three take together?

AdvancedTry it yourself first

A and B do a job in 9 days, B and C in 12 days and C and A in 18 days. How long will all three take together?

Leaving, joining and alternate days

Split the job into stages

Someone leaves or joins midway, workers alternate days, men and women are combined.

Leaving and joining

Add the work of each stage

Find the work done in each stage; the stages must add up to $1$ .

Cut the job into stages: “together”, “alone”, “newcomer joins”, and so on.
Work in a stage = (rate of that stage) $\times$ (its days).
Make the stages total $1$ and solve for the unknown.
If the total days are asked, do not forget to add the days of all stages.

Example 7 · Standard

A alone does a job in 20 days and B in 30 days. They start together and A leaves after 6 days. How many more days does B need?

Solution, step by step

1Work in 6 days $= 6 (\frac{1}{20} + \frac{1}{30}) = 6 \times \frac{1}{12} = \frac{1}{2}$ ; left $\frac{1}{2}$ .
2B: $\frac{1}{2} \times 30 = 15$ days

Answer 15 days

Example 8 · Standard

A alone does a job in 24 days and B in 8 days. A starts alone and B joins after 6 days. In how many days in all is the job done?

Solution, step by step

1A in 6 days: $\frac{6}{24} = \frac{1}{4}$ ; left $\frac{3}{4}$ .
2Joint rate $= \frac{1}{24} + \frac{1}{8} = \frac{1}{6}$ ; $\frac{3}{4} \div \frac{1}{6} = 4 \frac{1}{2}$ days; total $= 6 + 4 \frac{1}{2} = 10 \frac{1}{2}$ days

Answer $10 \frac{1}{2}$ days

BasicTry it yourself first

A alone can do a job in 12 days and B in 24 days. They start together and A leaves after 4 days. In how many more days does B finish the rest?

StandardTry it yourself first

A alone can do a job in 15 days and B in 20 days. They start together and A leaves after 6 days. In how many more days does B finish the rest?

StandardTry it yourself first

A alone can do a job in 18 days and B in 36 days. They start together and A leaves after 8 days. In how many more days does B finish the rest?

AdvancedTry it yourself first

A alone can do a job in 16 days and B in 40 days. They start together and A leaves after 5 days. In how many more days does B finish the rest?

AdvancedTry it yourself first

A alone can do a job in 20 days and B in 25 days. They start together and A leaves after 7 days. In how many more days does B finish the rest?

BasicTry it yourself first

A alone can do a job in 30 days and B in 15 days. A starts and B joins after 5 days. In how many days in all is the job finished?

StandardTry it yourself first

A alone can do a job in 20 days and B in 12 days. A starts and B joins after 4 days. In how many days in all is the job finished?

StandardTry it yourself first

A alone can do a job in 36 days and B in 18 days. A starts and B joins after 9 days. In how many days in all is the job finished?

AdvancedTry it yourself first

A alone can do a job in 28 days and B in 14 days. A starts and B joins after 10 days. In how many days in all is the job finished?

AdvancedTry it yourself first

A alone can do a job in 45 days and B in 15 days. A starts and B joins after 6 days. In how many days in all is the job finished?

BasicTry it yourself first

A alone does a job in 20 days and B in 25 days. A works 4 days and then B finishes the rest. How many days does B work?

StandardTry it yourself first

A alone does a job in 30 days and B in 24 days. A works 10 days and then B finishes the rest. How many days does B work?

StandardTry it yourself first

A alone does a job in 16 days and B in 40 days. A works 6 days and then B finishes the rest. How many days does B work?

AdvancedTry it yourself first

A alone does a job in 45 days and B in 36 days. A works 9 days and then B finishes the rest. How many days does B work?

BasicTry it yourself first

A worker does

\frac{1}{4}

of a job in 5 days. At the same pace in how many days is the whole job done?

StandardTry it yourself first

A worker does

\frac{2}{5}

of a job in 8 days. At the same pace in how many days is the whole job done?

StandardTry it yourself first

A worker does

\frac{3}{7}

of a job in 9 days. At the same pace in how many days is the whole job done?

AdvancedTry it yourself first

A worker does

\frac{5}{8}

of a job in 10 days. At the same pace in how many days is the whole job done?

Working on alternate days

The two-day cycle

Questions where workers take turns, one day each.

Make a two-day cycle: A’s work on day 1, B’s on day 2.
Work in one cycle $= \frac{1}{a} + \frac{1}{b}$ . See after how many whole cycles the job nearly finishes.
Finish the leftover at the rate of whoever works next — the last day may not be a full day.
Check: count days, not cycles.

Example 9 · Standard

A alone does a job in 10 days and B in 15 days. They work alternately a day each, A first. In how many days is the job done?

Solution, step by step

1One cycle (2 days) does $\frac{1}{10} + \frac{1}{15} = \frac{1}{6}$ .
25 cycles = 10 days do $\frac{5}{6}$ ; left $\frac{1}{6}$ . Day 11: A does $\frac{1}{10}$ ; then $\frac{1}{6} - \frac{1}{10} = \frac{1}{15}$ remains, exactly B’s whole day. Total $12$ days

Answer 12 days

BasicTry it yourself first

A alone can finish a job in 10 days and B in 15 days. They work on alternate days, A starting. In how many days is the job done?

BasicTry it yourself first

A alone can finish a job in 6 days and B in 12 days. They work on alternate days, A starting. In how many days is the job done?

StandardTry it yourself first

A alone can finish a job in 12 days and B in 18 days. They work on alternate days, A starting. In how many days is the job done?

StandardTry it yourself first

A alone can finish a job in 8 days and B in 20 days. They work on alternate days, A starting. In how many days is the job done?

AdvancedTry it yourself first

A alone can finish a job in 14 days and B in 21 days. They work on alternate days, A starting. In how many days is the job done?

AdvancedTry it yourself first

A alone can finish a job in 9 days and B in 15 days. They work on alternate days, A starting. In how many days is the job done?

Men, women and hours

The man-day unit

$M_{1} D_{1} H_{1} = M_{2} D_{2} H_{2}$ and “ $a$ men or $b$ women” questions.

∑ Formula

M_{1} D_{1} H_{1} \times W_{2} = M_{2} D_{2} H_{2} \times W_{1}

Men × days × hours ∝ work

Man-days are a unit of work: 5 men working 8 days give 40 man-days.
“ $a$ men or $b$ women” means $a$ men equal $b$ women in work, so 1 man $= \frac{b}{a}$ woman.
When work or hours change, always keep the total man-hours consistent.
If men leave midway, count the leftover in man-days and divide by the men remaining.

Example 10 · Basic

15 men harvest a field in 12 days. In how many days will 20 men do it?

Solution, step by step

1Total work $= 15 \times 12 = 180$ man-days.
220 men: $\frac{180}{20} = 9$ days — more men, fewer days ✓

Answer 9 days

Example 11 · Standard

8 men or 12 women do a job in 15 days. How long will 6 men and 6 women take together?

Solution, step by step

1One man’s day $= \frac{1}{120}$ , one woman’s $= \frac{1}{180}$ .
2Daily work $= \frac{6}{120} + \frac{6}{180} = \frac{1}{20} + \frac{1}{30} = \frac{1}{12}$ ⟹ $12$ days

Answer 12 days

BasicTry it yourself first

10 workers finish a job in 18 days. In how many days will 15 workers do the same job?

BasicTry it yourself first

12 workers finish a job in 20 days. In how many days will 16 workers do the same job?

StandardTry it yourself first

24 workers finish a job in 15 days. In how many days will 18 workers do the same job?

StandardTry it yourself first

9 workers finish a job in 28 days. In how many days will 14 workers do the same job?

AdvancedTry it yourself first

35 workers finish a job in 12 days. In how many days will 21 workers do the same job?

BasicTry it yourself first

8 men working 6 hours a day finish a job in 10 days. In how many days will 10 men working 8 hours a day do it?

StandardTry it yourself first

12 men working 8 hours a day finish a job in 15 days. In how many days will 18 men working 6 hours a day do it?

StandardTry it yourself first

20 men working 7 hours a day finish a job in 9 days. In how many days will 15 men working 6 hours a day do it?

AdvancedTry it yourself first

14 men working 9 hours a day finish a job in 18 days. In how many days will 21 men working 12 hours a day do it?

BasicTry it yourself first

6 men or 9 women do a job in 12 days. In how many days will 3 men and 3 women together do it?

StandardTry it yourself first

10 men or 15 women do a job in 18 days. In how many days will 5 men and 6 women together do it?

StandardTry it yourself first

4 men or 6 women do a job in 20 days. In how many days will 2 men and 3 women together do it?

AdvancedTry it yourself first

8 men or 12 women do a job in 30 days. In how many days will 4 men and 9 women together do it?

BasicTry it yourself first

24 men are to finish a job in 15 days. After 5 days, 4 men leave. In how many more days is the rest done?

StandardTry it yourself first

30 men are to finish a job in 20 days. After 8 days, 6 men leave. In how many more days is the rest done?

StandardTry it yourself first

20 men are to finish a job in 24 days. After 6 days, 10 men more join. In how many more days is the rest done?

AdvancedTry it yourself first

36 men are to finish a job in 30 days. After 10 days, 12 men more join. In how many more days is the rest done?

The LCM method

Make the total work a whole number

Take the total work as the LCM of the days and avoid fractions.

Total work = LCM

Think in units

Find each worker’s daily units; adding them gives the time directly.

Take the LCM of all the days — that is the total work (in units).
Each worker’s daily units = total work $\div$ his days.
Add the daily units; time = total work $\div$ units together.
Benefit: whole-number arithmetic without fractions; very fast in staged questions.

Example 12 · Standard

A, B and C alone do a job in 12, 20 and 30 days. Use the LCM method to find the time together.

Solution, step by step

1Total work $= LCM (12, 20, 30) = 60$ units; daily: A $5$ , B $3$ , C $2$ .
2Together $= 10$ units/day ⟹ $\frac{60}{10} = 6$ days

Answer 6 days

BasicTry it yourself first

A, B and C alone do a job in 6, 12 and 4 days. Taking the total work as the LCM, in how many days do all three finish it together?

BasicTry it yourself first

A, B and C alone do a job in 10, 15 and 30 days. Taking the total work as the LCM, in how many days do all three finish it together?

StandardTry it yourself first

A, B and C alone do a job in 12, 18 and 36 days. Taking the total work as the LCM, in how many days do all three finish it together?

StandardTry it yourself first

A, B and C alone do a job in 8, 24 and 12 days. Taking the total work as the LCM, in how many days do all three finish it together?

StandardTry it yourself first

A, B and C alone do a job in 20, 30 and 60 days. Taking the total work as the LCM, in how many days do all three finish it together?

AdvancedTry it yourself first

A, B and C alone do a job in 14, 21 and 42 days. Taking the total work as the LCM, in how many days do all three finish it together?

AdvancedTry it yourself first

A, B and C alone do a job in 15, 25 and 50 days. Taking the total work as the LCM, in how many days do all three finish it together?

Traps and fast tricks

Slips · tricks

Where marks go in work-and-time questions.

The commonest mistakes

Six traps

The slips that cost marks.

Trap 1Adding the days. Time together is not

a + b

; it is the one-day works that are added.

Trap 2Getting a larger time together. The time together is always less than the fastest worker’s time alone — if it comes out larger, stop and recheck.

Trap 3Forgetting to flip the fraction. If the one-day work comes to

\frac{5}{12}

after adding, the time is

\frac{12}{5}

days, not

\frac{5}{12}

days.

Trap 4Using the efficiency ratio as the time ratio. Someone 3 times as fast takes

\frac{1}{3}

of the time, not 3 times.

Trap 5Dropping a stage’s days. “Total days” must include the solo days as well.

Trap 6Counting the last day of an alternate-day job as a full day. Divide the leftover by the next worker’s rate.

Fast tricks

LCM and man-days

Habits for speed.

LCM units: take the LCM of the days as the total work; everything stays in whole numbers.
The pair formula: time together $\frac{ab}{a + b}$ — product ÷ sum.
$n$ equal workers take $\frac{1}{n}$ of one worker’s time together.
Man-days: when workers or work change, just keep the product equal.
Check: time together is below each one’s time alone; the day’s works add up to at most $1$ .

Example 13 · Standard

A+B do a job in 8 days, B+C in 12 days, and all three in 6 days. In how many days will A+C do it?

Solution, step by step

1Remove B+C from the trio: $A = \frac{1}{6} - \frac{1}{12} = \frac{1}{12}$ ; remove A+B: $C = \frac{1}{6} - \frac{1}{8} = \frac{1}{24}$ .
2 $A + C = \frac{1}{12} + \frac{1}{24} = \frac{3}{24} = \frac{1}{8}$ ⟹ $8$ days

Answer 8 days

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 finish a job in 10 days and B alone in 15 days. In how many days will they finish it working together?

BasicTry it yourself first

A alone can finish a job in 12 days and B alone in 6 days. In how many days will they finish it working together?

BasicTry it yourself first

A alone can finish a job in 8 days and B alone in 16 days. In how many days will they finish it working together?

BasicTry it yourself first

A alone can finish a job in 30 days and B alone in 20 days. In how many days will they finish it working together?

BasicTry it yourself first

A alone can finish a job in 24 days and B alone in 8 days. In how many days will they finish it working together?

BasicTry it yourself first

A and B together do a job in 10 days. A alone can do it in 30 days. In how many days can B alone do it?

BasicTry it yourself first

A and B together do a job in 6 days. A alone can do it in 9 days. In how many days can B alone do it?

BasicTry it yourself first

A and B together do a job in 8 days. A alone can do it in 24 days. In how many days can B alone do it?

BasicTry it yourself first

A, B and C can do a job alone in 4, 6 and 12 days. In how many days will they do it together?

BasicTry it yourself first

A, B and C can do a job alone in 9, 18 and 18 days. In how many days will they do it together?

BasicTry it yourself first

P is 2 times as efficient as Q and takes 5 days less. In how many days can P and Q each do the work alone?

BasicTry it yourself first

P is 3 times as efficient as Q and takes 10 days less. In how many days can P and Q each do the work alone?

BasicTry it yourself first

Kamal is 20% more efficient than Vimal. Vimal alone does a job in 24 days. In how many days can Kamal do it alone?

BasicTry it yourself first

Kamal is 25% more efficient than Vimal. Vimal alone does a job in 45 days. In how many days can Kamal do it alone?

BasicTry it yourself first

A alone can do a job in 10 days and B in 15 days. They start together and A leaves after 3 days. In how many more days does B finish the rest?

BasicTry it yourself first

A alone can do a job in 14 days and B in 28 days. They start together and A leaves after 4 days. In how many more days does B finish the rest?

BasicTry it yourself first

A alone can do a job in 24 days and B in 12 days. A starts and B joins after 6 days. In how many days in all is the job finished?

BasicTry it yourself first

A alone does a job in 12 days and B in 16 days. A works 3 days and then B finishes the rest. How many days does B work?

BasicTry it yourself first

A worker does

\frac{1}{3}

of a job in 6 days. At the same pace in how many days is the whole job done?

BasicTry it yourself first

A worker does

\frac{2}{3}

of a job in 8 days. At the same pace in how many days is the whole job done?

BasicTry it yourself first

A alone can finish a job in 8 days and B in 12 days. They work on alternate days, A starting. In how many days is the job done?

BasicTry it yourself first

A alone can finish a job in 5 days and B in 20 days. They work on alternate days, A starting. In how many days is the job done?

BasicTry it yourself first

12 workers finish a job in 25 days. In how many days will 20 workers do the same job?

BasicTry it yourself first

18 workers finish a job in 10 days. In how many days will 12 workers do the same job?

BasicTry it yourself first

6 men working 8 hours a day finish a job in 12 days. In how many days will 9 men working 6 hours a day do it?

BasicTry it yourself first

5 men or 10 women do a job in 24 days. In how many days will 2 men and 4 women together do it?

BasicTry it yourself first

20 men are to finish a job in 18 days. After 6 days, 4 men leave. In how many more days is the rest done?

BasicTry it yourself first

A, B and C alone do a job in 8, 12 and 24 days. Taking the total work as the LCM, in how many days do all three finish it together?

BasicTry it yourself first

A, B and C alone do a job in 9, 18 and 6 days. Taking the total work as the LCM, in how many days do all three finish it together?

BasicTry it yourself first

A and B do a job in 15 days, B and C in 20 days and C and A in 30 days. How long will all three take together?

Level 2 — Standard

Two ideas combined

Exam-level questions.

StandardTry it yourself first

A alone can finish a job in 18 days and B alone in 24 days. In how many days will they finish it working together?

StandardTry it yourself first

A alone can finish a job in 15 days and B alone in 25 days. In how many days will they finish it working together?

StandardTry it yourself first

A alone can finish a job in 10 days and B alone in 14 days. In how many days will they finish it working together?

StandardTry it yourself first

A alone can finish a job in 21 days and B alone in 28 days. In how many days will they finish it working together?

StandardTry it yourself first

A alone can finish a job in 16 days and B alone in 20 days. In how many days will they finish it working together?

StandardTry it yourself first

A and B together do a job in 18 days. A alone can do it in 45 days. In how many days can B alone do it?

StandardTry it yourself first

A and B together do a job in 10 days. A alone can do it in 25 days. In how many days can B alone do it?

StandardTry it yourself first

A and B together do a job in 20 days. A alone can do it in 36 days. In how many days can B alone do it?

StandardTry it yourself first

A, B and C can do a job alone in 10, 12 and 15 days. In how many days will they do it together?

StandardTry it yourself first

A, B and C can do a job alone in 6, 9 and 18 days. In how many days will they do it together?

StandardTry it yourself first

A, B and C can do a job alone in 20, 30 and 12 days. In how many days will they do it together?

StandardTry it yourself first

P is 3 times as efficient as Q and takes 12 days less. In how many days can P and Q each do the work alone?

StandardTry it yourself first

P is 2 times as efficient as Q and takes 9 days less. In how many days can P and Q each do the work alone?

StandardTry it yourself first

P is 5 times as efficient as Q and takes 8 days less. In how many days can P and Q each do the work alone?

StandardTry it yourself first

P is 4 times as efficient as Q and takes 18 days less. In how many days can P and Q each do the work alone?

StandardTry it yourself first

Kamal is 50% more efficient than Vimal. Vimal alone does a job in 60 days. In how many days can Kamal do it alone?

StandardTry it yourself first

Kamal is 60% more efficient than Vimal. Vimal alone does a job in 48 days. In how many days can Kamal do it alone?

StandardTry it yourself first

Kamal is 25% more efficient than Vimal. Vimal alone does a job in 75 days. In how many days can Kamal do it alone?

StandardTry it yourself first

A alone can do a job in 12 days and B in 30 days. They start together and A leaves after 5 days. In how many more days does B finish the rest?

StandardTry it yourself first

A alone can do a job in 24 days and B in 32 days. They start together and A leaves after 8 days. In how many more days does B finish the rest?

StandardTry it yourself first

A alone can do a job in 30 days and B in 45 days. They start together and A leaves after 9 days. In how many more days does B finish the rest?

StandardTry it yourself first

A alone can do a job in 24 days and B in 16 days. A starts and B joins after 6 days. In how many days in all is the job finished?

StandardTry it yourself first

A alone can do a job in 40 days and B in 20 days. A starts and B joins after 12 days. In how many days in all is the job finished?

StandardTry it yourself first

A alone does a job in 36 days and B in 45 days. A works 12 days and then B finishes the rest. How many days does B work?

StandardTry it yourself first

A alone does a job in 28 days and B in 35 days. A works 8 days and then B finishes the rest. How many days does B work?

StandardTry it yourself first

A worker does

\frac{3}{8}

of a job in 6 days. At the same pace in how many days is the whole job done?

StandardTry it yourself first

A worker does

\frac{4}{9}

of a job in 8 days. At the same pace in how many days is the whole job done?

StandardTry it yourself first

A alone can finish a job in 9 days and B in 18 days. They work on alternate days, A starting. In how many days is the job done?

StandardTry it yourself first

A alone can finish a job in 16 days and B in 24 days. They work on alternate days, A starting. In how many days is the job done?

StandardTry it yourself first

A alone can finish a job in 7 days and B in 14 days. They work on alternate days, A starting. In how many days is the job done?

StandardTry it yourself first

16 workers finish a job in 21 days. In how many days will 24 workers do the same job?

StandardTry it yourself first

25 workers finish a job in 18 days. In how many days will 30 workers do the same job?

StandardTry it yourself first

15 men working 6 hours a day finish a job in 12 days. In how many days will 20 men working 9 hours a day do it?

StandardTry it yourself first

9 men working 8 hours a day finish a job in 16 days. In how many days will 12 men working 6 hours a day do it?

StandardTry it yourself first

6 men or 8 women do a job in 24 days. In how many days will 3 men and 4 women together do it?

StandardTry it yourself first

12 men or 18 women do a job in 15 days. In how many days will 6 men and 6 women together do it?

StandardTry it yourself first

40 men are to finish a job in 24 days. After 10 days, 8 men leave. In how many more days is the rest done?

StandardTry it yourself first

18 men are to finish a job in 20 days. After 5 days, 6 men more join. In how many more days is the rest done?

StandardTry it yourself first

A, B and C alone do a job in 10, 12 and 15 days. Taking the total work as the LCM, in how many days do all three finish it together?

StandardTry it yourself first

A, B and C alone do a job in 9, 12 and 18 days. Taking the total work as the LCM, in how many days do all three finish it together?

StandardTry it yourself first

A and B do a job in 8 days, B and C in 12 days and C and A in 24 days. How long will all three take together?

StandardTry it yourself first

A and B do a job in 14 days, B and C in 21 days and C and A in 42 days. How long will all three take together?

Level 3 — Advanced

Many steps and clever thinking

Questions at the hard end of competitive exams.

AdvancedTry it yourself first

A alone can finish a job in 13 days and B alone in 17 days. In how many days will they finish it working together?

AdvancedTry it yourself first

A alone can finish a job in 22 days and B alone in 33 days. In how many days will they finish it working together?

AdvancedTry it yourself first

A alone can finish a job in 26 days and B alone in 39 days. In how many days will they finish it working together?

AdvancedTry it yourself first

A alone can finish a job in 9 days and B alone in 20 days. In how many days will they finish it working together?

AdvancedTry it yourself first

A and B together do a job in 15 days. A alone can do it in 33 days. In how many days can B alone do it?

AdvancedTry it yourself first

A and B together do a job in 24 days. A alone can do it in 56 days. In how many days can B alone do it?

AdvancedTry it yourself first

A and B together do a job in 12 days. A alone can do it in 28 days. In how many days can B alone do it?

AdvancedTry it yourself first

A, B and C can do a job alone in 14, 21 and 28 days. In how many days will they do it together?

AdvancedTry it yourself first

A, B and C can do a job alone in 12, 20 and 30 days. In how many days will they do it together?

AdvancedTry it yourself first

A, B and C can do a job alone in 18, 24 and 36 days. In how many days will they do it together?

AdvancedTry it yourself first

P is 3 times as efficient as Q and takes 16 days less. In how many days can P and Q each do the work alone?

AdvancedTry it yourself first

P is 5 times as efficient as Q and takes 20 days less. In how many days can P and Q each do the work alone?

AdvancedTry it yourself first

P is 4 times as efficient as Q and takes 21 days less. In how many days can P and Q each do the work alone?

AdvancedTry it yourself first

Kamal is 60% more efficient than Vimal. Vimal alone does a job in 56 days. In how many days can Kamal do it alone?

AdvancedTry it yourself first

Kamal is 20% more efficient than Vimal. Vimal alone does a job in 72 days. In how many days can Kamal do it alone?

AdvancedTry it yourself first

Kamal is 80% more efficient than Vimal. Vimal alone does a job in 90 days. In how many days can Kamal do it alone?

AdvancedTry it yourself first

A alone can do a job in 18 days and B in 27 days. They start together and A leaves after 6 days. In how many more days does B finish the rest?

AdvancedTry it yourself first

A alone can do a job in 24 days and B in 40 days. They start together and A leaves after 7 days. In how many more days does B finish the rest?

AdvancedTry it yourself first

A alone can do a job in 35 days and B in 28 days. They start together and A leaves after 9 days. In how many more days does B finish the rest?

AdvancedTry it yourself first

A alone can do a job in 33 days and B in 22 days. A starts and B joins after 11 days. In how many days in all is the job finished?

AdvancedTry it yourself first

A alone can do a job in 60 days and B in 20 days. A starts and B joins after 18 days. In how many days in all is the job finished?

AdvancedTry it yourself first

A alone does a job in 72 days and B in 48 days. A works 30 days and then B finishes the rest. How many days does B work?

AdvancedTry it yourself first

A alone does a job in 54 days and B in 63 days. A works 18 days and then B finishes the rest. How many days does B work?

AdvancedTry it yourself first

A worker does

\frac{7}{12}

of a job in 14 days. At the same pace in how many days is the whole job done?

AdvancedTry it yourself first

A worker does

\frac{5}{9}

of a job in 15 days. At the same pace in how many days is the whole job done?

AdvancedTry it yourself first

A alone can finish a job in 11 days and B in 22 days. They work on alternate days, A starting. In how many days is the job done?

AdvancedTry it yourself first

A alone can finish a job in 18 days and B in 27 days. They work on alternate days, A starting. In how many days is the job done?

AdvancedTry it yourself first

A alone can finish a job in 13 days and B in 26 days. They work on alternate days, A starting. In how many days is the job done?

AdvancedTry it yourself first

42 workers finish a job in 15 days. In how many days will 35 workers do the same job?

AdvancedTry it yourself first

28 workers finish a job in 33 days. In how many days will 44 workers do the same job?

AdvancedTry it yourself first

18 men working 9 hours a day finish a job in 14 days. In how many days will 24 men working 7 hours a day do it?

AdvancedTry it yourself first

25 men working 6 hours a day finish a job in 20 days. In how many days will 30 men working 8 hours a day do it?

AdvancedTry it yourself first

15 men or 20 women do a job in 24 days. In how many days will 9 men and 8 women together do it?

AdvancedTry it yourself first

9 men or 15 women do a job in 20 days. In how many days will 6 men and 10 women together do it?

AdvancedTry it yourself first

45 men are to finish a job in 36 days. After 12 days, 15 men leave. In how many more days is the rest done?

AdvancedTry it yourself first

30 men are to finish a job in 28 days. After 8 days, 20 men more join. In how many more days is the rest done?

AdvancedTry it yourself first

A, B and C alone do a job in 18, 24 and 36 days. Taking the total work as the LCM, in how many days do all three finish it together?

AdvancedTry it yourself first

A, B and C alone do a job in 16, 20 and 40 days. Taking the total work as the LCM, in how many days do all three finish it together?

AdvancedTry it yourself first

A and B do a job in 16 days, B and C in 24 days and C and A in 48 days. How long will all three take together?

AdvancedTry it yourself first

A and B do a job in 30 days, B and C in 40 days and C and A in 60 days. How long will all three take together?

Revision — formula cards

Flip each card and test yourself

Read the front, think, then flip.