Practice MCQ Questions and Answer on Time and Work

21.

2 men and 3 women together or 4 men can complete a piece of work in 20 days. 3 men and 3 women will complete the same work in = ?

(A) 12 days
(B) 16 days
(C) 18 days
(D) 19 days

Solution: According to the question, $\begin{aligned} 2m + 3w = 4m \\ 3w = 4m - 2m \\ 3w = 2m \\ 3m + 3w = 3m + 2m \\ 3m + 3w = 5m \end{aligned}$ 4 men can do work in 20 days 1 men can do work in 20 × 4 days 5 men can do work in $\frac{20 \times 4}{5}$ = 16 days $\begin{aligned} A l t e r n a t e : \\ (2 m + 3w) \times 20 = 4m \times 20 \\ \frac{m}{w} = \frac{3}{2} \\ Total work \\ = (2 \times 3 + 3 \times 2) \times 20 \\ = 240 units \\ 5 men efficiency \\ = 5 \times 3 \\ = 15 \\ Required number of days \\ = \frac{240}{15} \\ = 16 days \end{aligned}$

22.

Two worker A and B are engaged to do a piece of work. A working alone would take 8 hours more to complete the work that when work together. If B worked alone, would take $4 \frac{1}{2}$ hours more than when working together. The time required to finish the work together is = ?

(A) 5 hours
(B) 8 houras
(C) 4 hours
(D) 6 hours

Solution: $\begin{aligned} Let, \\ a = 8h \\ b = 4 \frac{1}{2} h = \frac{9}{2} h \end{aligned}$ Time required to finish the work together $\begin{aligned} = \sqrt{ab} \\ = \sqrt{8 \times \frac{9}{2}} \\ = 6 h \end{aligned}$

23.

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%

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%

24.

A complete $\frac{7}{10}$ of a work in 15 days, then he completed the remaining work with the help of B in 4 days. In how many day A and B can complete entire work together?

(A) $10 \frac{1}{2} days$
(B) $12 \frac{2}{3} days$
(C) $13 \frac{1}{3} days$
(D) $8 \frac{1}{4} days$

Solution: $\frac{7}{10}$ part of work has been completed by A in 15 days. Then, Rest work = 1 - $\frac{7}{10}$ = $\frac{3}{10}$ part Given, That $\frac{3}{10}$ part of the work is completed by A and B together in 4 days. Means, (A + B) completed the $\frac{3}{10}$ of work in 4 days So, (A + B)'s 1 day's work = $\frac{3}{10 \times 4}$ = $\frac{3}{40}$ Hence, (A + B) can complete the work in $\frac{40}{3}$ = $13 \frac{1}{3}$ days

25.

A man is twice as fast as a women and a woman is twice as fast as a boy in doing a work. If all of them, a man , a woman and a boy can finish the work in 7 days, a boy will do it alone ?

(A) 49 days
(B) 7 days
(C) 6 days
(D) 42 days

Solution: Man : Woman : Boy Efficiency 4 : 2 : 1 Total work = Time × (Efficiency of man + woman + boy) ⇒ 7 days × (4 + 2 + 1) = 49 units ∴ Boy can do this work in = $\frac{49}{1}$ = 49 days

26.

Tapas works twice as fast as Mihir. If both of them together complete a work in 12 days, Tapas alone can complete it in ?

(A) 15 days
(B) 18 days
(C) 20 days
(D) 24 days

Solution: Tapas : Mihir Efficiencyunits/day 2 : 1 $\begin{aligned} T + M complete in 12 days \\ Total work \\ = 12 \times (2 + 1) \\ = 36 units \end{aligned}$ Tapas alone complete the whole work in $\begin{aligned} = \frac{36}{2} \\ = 18 days \end{aligned}$

27.

Ten men begin to do a work. But after some days, four of them left the job. As a result, the job that could have been completed in 40 days is completed in 50 days. How many days after the commencement of the work did the four men leave?

(A) 30
(B) 20
(C) 35
(D) 25

28.

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

29.

A single reservoir supplies the petrol to the whole city, while the reservoir is fed by a single pipeline filling the reservoir with the stream of uniform volume. When the reservoir is full and if 40, 000 litres of petrol is used daily, the supply fails in 90 days. If 32, 000 litres of petrol used daily, it fails in 60 days. How much petrol can be used daily without the supply ever failing?

(A) 64000 litres
(B) 56000 litres
(C) 60000 litres
(D) 78000 litres

30.

A group of workers can complete a piece of work in 50 days, when they are working individually. On the first day one person works, on the second day another person joins him, on the third day one person joins them and this process continues till the work is completed. How many approximate days are needed to complete the work ?

(A) 8 days
(B) 9 days
(C) 10 days
(D) 11 days

Solution: Let a man complete 1 piece of work in a day. Then total work = 50 units Then by statement 1 st day = one man × 1 work/day = 1 Then by statement 2nd day = two men × 1 work/day = 2 Then by statement 3rd day = three men × 1 work/day = 3 Let the whole work will be completed in N days. Then total work 1 + 2 + 3 + ..... + N = 50 $\begin{aligned} \frac{N (N + 1)}{2} = 50 \\ N (N + 1) = 100 \\ Then, N = 10 days (approx) \end{aligned}$

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Practice MCQ Questions and Answer on Time and Work

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