A can do a piece of work in 10 days and B in 15 days. Working together, in how many days will they finish it?

6 days. Together their one day's work is 110 + 115 = 16, so they finish in 6 days.

A can complete a job in 12 days. He works for 3 days and then leaves. What fraction of the job is left?

34. In 3 days he does 312 = 14 of the job, so 34 remains.

A and B together can do a job in 8 days, and B alone can do it in 24 days. How long does A alone take?

12 days. A's one day's work = 18 - 124 = 112, so A alone takes 12 days.

A is twice as efficient as B, and together they finish a job in 12 days. How long does B alone take?

36 days. If B does 1 unit a day, A does 2, so together 3 units a day. The job is 3 12 = 36 units, which B alone does in 36 days.

A can do a work in 20 days and B in 30 days. They start together, but A leaves 5 days before the work is finished. In how many days is the work completed?

15 days. If the work ends in T days, A works T - 5 days and B works T days: T - 520 + T30 = 1. Then 3(T - 5) + 2T = 60, so 5T = 75 and T = 15 days.

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Quantitative Aptitude · Time, Work & Distance

Time and Work — Questions & Answers

Time-and-work questions treat a job as one whole unit and each worker as a rate — the fraction of the job done per day. Add rates when people work together; subtract for a leak or an opposing worker.

5 solved questions
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Key formulas included

Key formulas

If A finishes a job in $a$ days, A's one day's work is $\dfrac{1}{a}$
Together: one day's work $= \dfrac{1}{a} + \dfrac{1}{b}$ , so time $= \dfrac{ab}{a+b}$
Men–days: $M_1 D_1 = M_2 D_2$ for the same job (add hours per day as another factor if given)

5 solved Time and Work questions

Try each question first — tap an option to check your answer, or open Learn step by step for a guided walkthrough.

01
A can do a piece of work in 10 days and B in 15 days. Working together, in how many days will they finish it?
4 steps · reveal one at a time
1. Step 1: **Individual Work Rates**
  First, let's find out how much work each person does in one day. If A finishes the work in 10 days, A completes $1/10$ of the work per day. Similarly, B completes $1/15$ of the work per day.
2. Step 2: **Combined Daily Work**
  When A and B work together, their daily work rates add up. So, their combined work per day is the sum of their individual rates: $1/10 + 1/15$ . To add these fractions, find a common denominator, which is 30. This gives us $3/30 + 2/30 = 5/30$ .
3. Step 3: **Total Time Taken**
  The combined daily work simplifies to $5/30 = 1/6$ . This means that together, A and B complete $1/6$ of the work each day. To find the total number of days they will take to finish the entire work, we take the reciprocal of their combined daily work rate.
4. Step 4: The answer
  So the answer is (B) 6 days. The reciprocal of $1/6$ is 6, meaning they will finish the work in 6 days when working together.
02
A can complete a job in 12 days. He works for 3 days and then leaves. What fraction of the job is left?
5 steps · reveal one at a time
1. Step 1: Daily Work Rate
  First, figure out how much of the job A completes in one day. If A finishes the whole job in 12 days, then in one day, A completes $1/12$ of the job.
2. Step 2: Work Done
  A works for 3 days. To find the total work A completed, multiply the daily work rate by the number of days worked. Work done $= 3 \times (1/12)$ .
3. Step 3: Simplify Fraction
  Simplify the fraction of the job A completed. $3 \times (1/12) = 3/12$ . This fraction can be simplified by dividing both numerator and denominator by 3, which gives $1/4$ .
4. Step 4: Remaining Work
  The question asks for the fraction of the job left. If $1/4$ of the job is completed, subtract this from the total job (which is 1). Remaining job $= 1 - 1/4$ .
5. Step 5: The answer
  So the answer is (C) $\dfrac{3}{4}$ . When you subtract $1/4$ from $1$ (or $4/4$ ), you are left with $3/4$ of the job.
03
A and B together can do a job in 8 days, and B alone can do it in 24 days. How long does A alone take?
4 steps · reveal one at a time
1. Step 1: Understand Work Rates
  When solving work problems, it's helpful to think about how much of the job is done in one day. If someone completes a job in $X$ days, their one day's work is $1/X$ of the total job.
2. Step 2: Calculate Daily Work
  We know A and B together complete the job in 8 days. So, their combined one day's work is $1/8$ . B alone completes the job in 24 days, meaning B's one day's work is $1/24$ .
3. Step 3: Find A's Daily Work
  To find how much work A does in one day, we subtract B's daily work from their combined daily work. A's one day's work $= \frac{1}{8} - \frac{1}{24}$ .
4. Step 4: The answer
  So the answer is (D) 12 days. Performing the subtraction, A's one day's work is $\frac{3}{24} - \frac{1}{24} = \frac{2}{24} = \frac{1}{12}$ . If A does $1/12$ of the job per day, A takes 12 days to complete the job alone.
04
A is twice as efficient as B, and together they finish a job in 12 days. How long does B alone take?
4 steps · reveal one at a time
1. Step 1: Define efficiency
  Let's assume B completes $1$ unit of work per day. Since A is twice as efficient as B, A completes $2$ units of work per day.
2. Step 2: Calculate combined rate
  When A and B work together, their combined work rate is the sum of their individual rates. This means they complete $1 + 2 = 3$ units of work per day.
3. Step 3: Determine total work
  They finish the entire job in $12$ days, working at a combined rate of $3$ units per day. So, the total work required for the job is $3 \times 12 = 36$ units.
4. Step 4: The answer
  So the answer is (B) 36 days. Since B completes $1$ unit of work per day, B alone would take $36 \div 1 = 36$ days to complete the entire job.
05
A can do a work in 20 days and B in 30 days. They start together, but A leaves 5 days before the work is finished. In how many days is the work completed?
5 steps · reveal one at a time
1. Step 1: Understand work rates
  First, let's determine the work rate for each person. A can do the work in 20 days, so A's daily work rate is $1/20$ . B can do the work in 30 days, so B's daily work rate is $1/30$ .
2. Step 2: Define total time
  Let $T$ be the total number of days the work is completed. We know A leaves 5 days before the work finishes, so A works for $T - 5$ days. B works for the entire duration, which is $T$ days.
3. Step 3: Formulate the equation
  The total work done is the sum of the work done by A and B. A completes $(T - 5)/20$ of the work, and B completes $T/30$ of the work. Since the entire work is completed, we set the sum equal to 1: $(T - 5)/20 + T/30 = 1$ .
4. Step 4: Solve for T
  To solve for $T$ , find a common denominator (60) and multiply the equation: $3(T - 5) + 2T = 60$ . This simplifies to $3T - 15 + 2T = 60$ . Combine terms to get $5T - 15 = 60$ . Add 15 to both sides: $5T = 75$ . Finally, divide by 5 to find $T = 15$ days.
5. Step 5: The answer
  So the answer is (C) 15 days. The calculation shows that the total time taken to complete the work is 15 days, which matches this option.

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