Quantitative Aptitude

Time and Work

2,195 Questions
All Pairwise rates and staged schedules 440 Workers-days-hours chain rule 439 LCM units and efficiency ratios 409 Different worker categories 311 Combined rates and an unknown worker 257 Division of wages 219 Alternate work 110 Opposing rates 10

Time and Work Questions

Multiple choice

$A$ does $80$% of a work in $20$ days. He then calls in $B$ and they together finish the remaining work in $3$ days. How long $B$ alone would take to do the whole work?
  1. $23$ days
  2. $37$ days
  3. $37\cfrac{1}{2}$
  4. $40$ days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A does 80% in 20 days, so A's rate is 4% per day. Remaining 20% is done by A and B in 3 days, so (A+B)'s rate is 20/3 = 6.66% per day. B's rate = 6.66 - 4 = 2.66% per day. Time for B = 100 / 2.66 = 37.5 days.

Multiple choice

$A$ and $B$ together can complete a task in $7$ days. $B$ alone can do it in $20$ days. What part of the work was carried out by $A$? $I$. $A$ completed the job alone after $A$ and $B$ worked together for $5$ days. $II$. Part of the work done by $A$ could have been done by $B$ and $C$ together in $6$ days.
  1. $I$ alone sufficient while $II$ alone not sufficient to answer
  2. $II$ alone sufficient while $I$ alone not sufficient to answer
  3. Either $I$ or $II$ alone sufficient to answer
  4. Both $I$ and $II$ are not sufficient to answer
  5. Both $I$ and $II$ are necessary to answer
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Statement I: A+B take 7 days. If they work 5 days, they finish 5/7 of the work. A finishes the remaining 2/7 alone. This is sufficient. Statement II: Does not provide enough info to isolate A's work.

Multiple choice

$A$ can finish a work in $24$ days, $B$ in $9$ days and $C$ in $12$ days. $B$ and $C$ start the work but are force to leave after $3$ days. The remaining work was done by $A$ in:
  1. $5$ days
  2. $6$ days
  3. $10$ days
  4. $10\cfrac{1}{2}$ days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A's work rate is 1/24, B's is 1/9, C's is 1/12. B and C work for 3 days, completing 3 * (1/9 + 1/12) = 3 * (4/36 + 3/36) = 3 * (7/36) = 7/12 of the work. Remaining work is 1 - 7/12 = 5/12. A completes this in (5/12) / (1/24) = 5/12 * 24 = 10 days.

Multiple choice

In how many days can $10$ women finish a work? $I$. $10$ men can complete the work in $6$ days. $II$. $10$ men and $10$ women together can complete the work in $3\cfrac{3}{7}$ days. $III$. If $10$ men work for $3$ days and thereafter $10$ women replace them, the remaining work in completed in $4$ days.

  1. Any two of the three
  2. $I$ and $II$ only
  3. $II$ and $III$ only
  4. $I$ and $III$ only

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let M be men's rate, W be women's rate. I: 10M = 1/6. II: 10M + 10W = 1/(24/7) = 7/24. III: 10M*3 + 10W*4 = 1. Any two of these equations allow solving for M and W, thus finding the time for 10 women (1/W).

Multiple choice

$X$ can do a piece work in $40$ days. He works at it for $8$ days and then $Y$ finished it in $16$ days. How long will they together take to complete the work?
  1. $13\cfrac{1}{3}$ days
  2. $15$ days
  3. $20$ days
  4. $26$ days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

X does 1/40 of work per day. In 8 days, X does 8/40 = 1/5 of the work. Remaining work = 4/5. Y finishes 4/5 in 16 days, so Y does (4/5)/16 = 1/20 of the work per day. Together, they do 1/40 + 1/20 = 3/40 of the work per day. Time taken = 40/3 = 13 1/3 days.

Multiple choice

How many worker are required for completing the construction work in $10$ days? $I$. $20$% of the work can be completed by $8$ workers in $8$ days. $II$. $20$ workers can complete the work in $16$ days. $III$. One-eighth of the work can be completed by $8$ workers in $5$ days.
  1. $I$ only
  2. $II$ and $III$ only
  3. $III$ only
  4. $I$ and $III$ only

  5. Any one of the three
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

All three statements provide enough information to calculate the total work capacity and thus the number of workers required for 10 days. I: 20% in 8 days by 8 workers -> 100% in 40 days by 8 workers -> 10 days by 32 workers. II: 20 workers in 16 days -> 10 days by 32 workers. III: 1/8 in 5 days by 8 workers -> 100% in 40 days by 8 workers -> 10 days by 32 workers.

Multiple choice

$8$ men and $14$ women are working together in a field. After working for $3$ days, $5$ men and $8$ women leave the work. How many more days will be required to complete the work? $I$. $19$ men and $12$ women together can complete the work in $18$ days. $II$. $16$ men can complete two-third of the work in $16$ days. $III$. In $1$ day, the work done by three men in equal to the work done by four women.
  1. $I$ only
  2. $II$ only
  3. $III$ only
  4. $I$ or $II$ or $III$
  5. $II$ or $III$ only
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

A can do a piece of work in $20$ days B in $15$ days and C in $12$ days. How soon can the work be done if A is assisted by B on one day and by C on the next alternately?
  1. $14$ days
  2. $6$ days
  3. $8$ days
  4. $10$ days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A's work rate is 1/20, B's is 1/15, and C's is 1/12. On day 1, A and B work together (1/20 + 1/15 = 7/60); on day 2, A and C work together (1/20 + 1/12 = 8/60). In 2 days, they complete 15/60 = 1/4 of the work, so the total work takes 8 days.

Multiple choice

A can do a piece of work in $6\dfrac {2}{3}$ days and B in $5$ days. They work together for $2$ days and then A leaves B to finish the work alone. How long will B take to finish it?
  1. $\dfrac {3}{4}$ days
  2. $1\dfrac {1}{2}days$
  3. $3\ days$
  4. $7\ days$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A's rate = 1 / (20/3) = 3/20 work/day. B's rate = 1/5 = 4/20 work/day. Combined rate = 7/20 work/day. Work done in 2 days = 2 * (7/20) = 14/20 = 7/10. Remaining work = 3/10. B finishes 3/10 at rate 1/5: (3/10) / (1/5) = 15/10 = 1.5 days.