Time & Work Questions and Answers

Answer: B

The fraction of work left is 8/15.

Ajit does \(\frac{1}{15}\) of the work a day and Dev \(\frac{1}{20}\).

\[ \begin{aligned} \text{one day} &= \frac{1}{15} + \frac{1}{20} = \frac{7}{60} \\ \text{4 days} &= \frac{28}{60} = \frac{7}{15} \\ \text{left} &= 1 - \frac{7}{15} = \frac{8}{15} \end{aligned} \]

7/15 is the work done in four days, not the work left, which is the trap in option A.

Answer: B

B alone can do the work in 24 days.

Add the three pairs' daily work. Each person is counted twice, so this is twice the work of A, B and C together:

\[ \begin{aligned} 2(A + B + C) &= \frac{1}{18} + \frac{1}{12} + \frac{1}{9} = \frac{1}{4} \\ A + B + C &= \frac{1}{8} \\ B &= \frac{1}{8} - \frac{1}{12} = \frac{1}{24} \end{aligned} \]

Here \(\frac{1}{12}\) is the work of A and C together. So B does \(\frac{1}{24}\) of the work a day and needs 24 days. 18 days is the time for A and B together, not for B alone.

Answer: C

P takes 12 hours.

Find each rate in pages per hour:

\[ \begin{aligned} S &= \frac{50}{10} = 5 \\ S + P &= \frac{300}{40} = 7.5 \\ P &= 2.5 \end{aligned} \]

So P copies 30 pages in \(\frac{30}{2.5} = 12\) hours. The other options do not match a rate of 2.5 pages an hour.

Check: in 40 hours S copies \(5 \times 40 = 200\) pages and P copies \(2.5 \times 40 = 100\), which together make the 300 pages stated.

Answer: A

He can finish half the work in 8 days.

If three quarters of the work takes 12 days, a quarter takes 4 days and the whole work 16 days.

\[ \begin{aligned} \tfrac{3}{4} \text{ work} &= 12 \text{ days} \\ 1 \text{ work} &= 12 \times \tfrac{4}{3} = 16 \text{ days} \\ \tfrac{1}{2} \text{ work} &= 16 \times \tfrac{1}{2} = 8 \text{ days} \end{aligned} \]

6 days is half of 12, which wrongly treats 12 days as the time for the whole work. 4 days is one quarter of the work, and 9 days comes from multiplying 12 by 3/4.

Answer: B

20 men will finish the work in 9 days.

The total work is fixed, measured in man-days, so more men take proportionally fewer days:

\[ \begin{aligned} \text{Work} &= 12 \times 15 = 180 \text{ man-days} \\ \text{Days} &= \frac{180}{20} = 9 \end{aligned} \]

Check: 20 men for 9 days is 180 man-days, the same as 12 men for 15 days.

8 days would give only 160 man-days and 10 or 11 days more than 180, so they do not match the same work.

Answer: B

Rindia can do a job in 10 days.
So efficiency of Rindia = 100/10 = 10%
Similarly, Rakesh's efficiency = 100/5 = 20%
Combined efficiency of Rindia + Rakesh per day becomes = 20 + 10 = 30 %
Now, we have to find out the number of days taken by both Rindia and Rakesh to do 100% work,
Since they can do 30% work in 1 day,
So, they will 100% work in 100/30 = 3.33 days

Answer: D

A completes the work in 30 days. A's one day work will be 1/30 of the work. B's one day work will be 1/45 of the work.
Both work together, in one day, 1/30 + 1/45 of the work will get over.
In one day 75/1350 of the work will get over. Which means the work will get over in 1350/75 days. The work will get completed in 18 days.

Answer: B

Together, A & B will finish the work in 7.2 days.

Answer: C

A completes the work in 24 days. A's one day work will be 1/24 of the work.
B's one day work will be 1/12 of the work.
Both work together, in one day, 1/24 + 1/12 of the work will get over.
In one day 36/288 of the work will get over. Which means the work will get over in 288/36 days.
The work will get completed in 8 days.

Answer: B

All three together finish in 4 days, so their combined rate is \( \tfrac{1}{4} \).

\[ \frac{1}{10} + \frac{1}{20} = \frac{2 + 1}{20} = \frac{3}{20} \]

\[ \frac{1}{C} = \frac{1}{4} - \frac{3}{20} = \frac{5 - 3}{20} = \frac{1}{10} \]

\[ C = 10 \text{ days} \]