Time And Work - Aptitude MCQ Questions and Solutions with Explanations

21

A certain number of persons can complete a work in 34 days working 9 h a day. If the number of persons is decreased by 40%. Then how many hours a day should the remaining persons work to complete the work in 51 days?

A) 9 B) 10 C) 8 D) 12

Discuss

Answer & Solution

Answer: Option B

Solution:

\[40\% \to \frac{{ - 2}}{5}\begin{array}{*{20}{c}} {} \\ { \to \,{\text{Men}}} \end{array}\]
$$\eqalign{ & 9 \times 34 \times 5 = 3 \times 51 \times x \cr & x = 10{\text{ hours}} \cr} $$

22

There are 3 taps A, B, and C in a tank. These can fill the tank in 10 hours, 20 hours and 25 hours, respectively. At first, all three taps are opened simultaneously. After 2 hours, tap C is closed and A and B keep running. After 4 hours from the beginning, tap B is also closed. The remaining tank is filled by tap A alone. Find the percentage of work done by tap A itself.

A) 32% B) 75% C) 52% D) 72%

Discuss

Answer & Solution

Answer: Option D

Solution:

2 hours total → 2 × 19 = 38
4 hours total = 38 + 2 × 15 = 68
Remaining work = 100 - 68 = 32
Total work done by A = 32 + 40 = 72
Required % = $$\frac{{72}}{{100}}$$ × 100 = 72%

23

P can finish a work in 18 days. When he had worked for 5 days, Q joined him. If both of them together completed the remaining work in $$\frac{{13}}{5}$$ days, then in how many days can Q alone finish $$66\frac{2}{3}\% $$ of the same work?

A) 2 B) 3 C) 4 D) 5

Discuss

Answer & Solution

Answer: Option B

Solution:

$$\eqalign{ & {\text{Total work}} = 18P = 5P + \frac{{13}}{5}\left( {P + Q} \right) \cr & 13P = \frac{{13}}{5}P + \frac{{13}}{5}Q \cr & \frac{{52}}{5}P = \frac{{13}}{5}Q \cr & \frac{P}{Q} = \frac{1}{4} \cr & {\text{Total work}} = 18 \times 1 = 18 \cr & 66\frac{2}{3}\% {\text{ of work}} = \frac{2}{3} \times 18 = 12 \cr & Q{\text{ days}} = \frac{{12}}{4} = 3{\text{ days}} \cr} $$

24

A man, a woman and a boy can complete a work in 3, 4 and 12 days, respectively. How many boys must assist one man and one woman to complete the same work in one day?

A) 5 B) 7 C) 4 D) 9

Discuss

Answer & Solution

Answer: Option A

Solution:

Total work for 1Men + 1Women + xBoy in 1 day = 12
⇒ 1 × 4 + 1 × 3 + 1 × x = 12
⇒ x = 12 - 7
⇒ x = 5

25

5 men and 8 women can complete a task in 34 days, whereas 4 men and 18 women can complete the same task in 28 days. In how many days can the same task be completed by 3 men and 5 women?

A) 64 B) 72 C) 56 D) 36

Discuss

Answer & Solution

Answer: Option C

Solution:

(5M + 8W) × 34 = (4M + 18W) × 28
85M + 136W = 56M + 252W
29M = 116W
$$\frac{{\text{M}}}{{\text{W}}} = \frac{4}{1}$$
(5M + 8W) × 34 = (3M + 5W) × x
(5 × 4 + 8 × 1) × 34 = (3 × 4 + 5 × 1) × x
28 × 34 = 17 × x
x = 56 days

26

B would have taken 10 hours more than what A would have taken to complete a task if each of them worked alone. Working together they can complete the task in 12 hours. How many hours would B take to do 50% of the task?

A) 30 B) 15 C) 20 D) 10

Discuss

Answer & Solution

Answer: Option B

Solution:

Let A completes the work in $$x$$ hours
∴ B completes the work in $$x$$ + 10 hours
Time and Work mcq question image

⇒ A + B complete the work in 12 hours
$$\eqalign{ & \therefore \frac{{x\left( {10 + x} \right)}}{{10 + x + x}} = 12 \cr & 10x + {x^2} = 120 + 24x \cr & {x^2} - 14x - 120 = 0 \cr} $$
On solving, $$x$$ = 20 hours
∴ B will complete whole work in 20 + 10 = 30 hours
Hence, 50% of work will be completed in 15 hours

27

Smith and Ajit can complete a task in 12 days and 18 days, respectively. If they work together on the task for 4 days, then the fraction of the task that will be left is:

A) $$\frac{5}{9}$$ B) $$\frac{2}{9}$$ C) $$\frac{1}{9}$$ D) $$\frac{4}{9}$$

Discuss

Answer & Solution

Answer: Option D

Solution:

(Smith + Ajit) × 4 = 4 × 5 = 20
Remaining work = 36 - 20 = 16
Then the fraction of the task that will be left is $$ = \frac{{16}}{{36}} = \frac{4}{9}$$

28

If 6 women can complete a work in 3 days, and 9 girls can complete the same work in 2 days, then find the time taken to complete the same work by 8 women and 6 girls?

A) 3 days B) 4 days C) 6 days D) $$\frac{9}{7}$$ days

Discuss

Answer & Solution

Answer: Option D

Solution:

$$\eqalign{ & 6W \times 3 = 9G \times 2 \cr & \frac{W}{G} = \frac{1}{1} \cr & {\text{Total work}} = 18 \cr & 18 = \left( {8W + 6G} \right) \times d \cr & 18 = 14 \times d \cr & d = \frac{9}{7}{\text{ days}} \cr} $$

29

A, B and C can do a work separately in 18, 36 and 54 days, respectively. They started the work together, but B and C left 5 days and 10 days, respectively, before the completion of the work. In how many days was the work finished?

A) 15 days B) 13 days C) 14 days D) 12 days

Discuss

Answer & Solution

Answer: Option B

Solution:

If B worked 5 days more = 3 × 5 = 15 unit
If C worked 10 days more = 2 × 10 = 20 unit
Now, total work = 108 + 15 + 20 = 143
(A + B + C) = $$\frac{{143}}{{11}}$$ = 13 days

30

Amir and Akbar can finish a task in 30 days and 15 days, respectively. Akbar worked on the task for 8 days and left the job. In how many days can Amir alone finish the remaining work?

A) 14 days B) 15 days C) 16 days D) 17 days

Discuss

Answer & Solution

Answer: Option A

Solution:

Akbar's 8 days work = 8 × 2 = 16
Remaining work = 30 - 16 = 14