Practice MCQ Questions and Answer on Time and Work

251.

A can complete work in 25 days and B can complete the same work in 20 days. They started the work together but B left after 4 days and A continued to work. In how many days will the entire work be completed?

(A) 25
(B) 20
(C) 28
(D) 22

Solution: Total work of (A + B) in 4 days = 4(4 + 5) = 36 Remaining work = 100 - 36 = 64 A = $\frac{64}{4}$ = 16 days Total days = 4 + 16 = 20 days

252.

Anuj and Manoj can together paint their house in 30 days. After working for 20 days, Anuj has to go out and Manoj finished the remaining working the next 30 days. If Manoj had gone away after 20 days instead of Anuj, then Anuj would have completed the remaining work in ?

(A) 15 days
(B) 20 days
(C) 25 days
(D) 35 days

Solution: $\begin{aligned} (Anuj + Manoj)'s 20 day's work \\ = (\frac{1}{30} \times 20) \\ = \frac{2}{3} \\ Remaining work \\ = (1 - \frac{2}{3}) \\ = \frac{1}{3} \\ Manoj's 30 day's work = \frac{1}{3} \\ ∴ Manoj's 1 day's work = \frac{1}{90} \\ Anuj's 1 day's work \\ = (\frac{1}{30} - \frac{1}{90}) \\ = \frac{2}{90} \\ = \frac{1}{45} \end{aligned}$ If Manoj had gone away after 20 days, then the remaining $\frac{1}{3}$ work would have been done by Anuj. $\frac{1}{45}$ work is done by Anuj in 1 day $\frac{1}{3}$ work would be done by Anuj in $\begin{aligned} = (45 \times \frac{1}{3}) \\ = 15 days \end{aligned}$

253.

A can do a piece of work in 12 days while B alone can do it in 15 days. With the help of C they can finish it in 5 days. If they are paid Rs. 960 for the whole work. How much money A gets ?

(A) Rs. 480
(B) Rs. 240
(C) Rs. 320
(D) Rs. 400

Solution: (A + B)'s 1 day work $\begin{aligned} = \frac{1}{12} + \frac{1}{15} \\ = \frac{5 + 4}{60} \\ = \frac{9}{60} = \frac{3}{20} \end{aligned}$ (A + B + C)'s 1 day work = $\frac{1}{5}$ ∴ C's 1 day work $\begin{aligned} = \frac{1}{5} - \frac{3}{20} \\ = \frac{4 - 3}{20} \\ = \frac{1}{20} \end{aligned}$ Ratio of their work $\begin{aligned} = \frac{1}{12} : \frac{1}{15} : \frac{1}{20} \\ = 5 : 4 : 3 \end{aligned}$ $\begin{aligned} A's share = \frac{5}{12} \times 960 \\ = Rs . 400 \end{aligned}$

254.

Kiran, Vishal and Dinesh work in a juice factory. Kiran takes 2 hours to extract as much juice as Vishal can in 3 hours. Dinesh takes 5 hours to extract as much juice that Kiran extracts in 4 hours. A tank can be filled with juice in 48 hours, if all of them work together. How long will it take to fill the tank, if Dinesh alone is trying to fill the tank?

(A) 132 hrs
(B) 148 hrs
(C) 140 hrs
(D) 135 hrs

Solution: $\begin{aligned} 3 \times V = 2 \times K \\ \frac{V}{K} = \frac{2}{3} = \frac{10}{15} \\ 4 \times K = D \times 5 \\ \frac{K}{D} = \frac{5}{4} = \frac{15}{12} \\ Total work = 48 \times (10 + 15 + 12) \\ Time of Dinesh = (\frac{48 \times 37}{12}) = 148 hr \end{aligned}$

255.

If 3 men or 4 women can plough a field in 43 days, how long will 7 men and 5 women take to plough it?

(A) 10 days
(B) 11 days
(C) 9 days
(D) 12 days

Solution: 3 men or 4 women can plough the field in 43 days 3 men = 4 women 1 man = $\frac{4}{3}$ women 7 man = $\frac{28}{3}$ women 7 men and 5 women = $5 + \frac{28}{3}$ = $\frac{43}{3}$ women 4 women can plough field in 43 days So, 1 women can plough in = 43 × 4 days Hence, $\frac{43}{3}$ women can plough = $\frac{43 \times 4 \times 3}{43}$ = 12 days

256.

A and B undertake a piece of work for Rs. 250. A alone can do that work in 5 days and B alone can do that work in 15 days. With the help of C, they finish the work in 3 days. If every one gets paid in proportion to work done by them, the amount C will get is ?

(A) Rs. 50
(B) Rs. 100
(C) Rs. 150
(D) Rs. 200

Solution: L.C.M. of Total Work = 45 One day work of A = $\frac{45}{5}$ = 9 unit/day One day work of B = $\frac{45}{15}$ = 3 unit/day One day work of A + B + C = $\frac{45}{3}$ = 15 unit/day $\begin{aligned} Efficiency of C \\ = 15 - (9 + 3) \\ = 3 \\ C's amount \\ = \frac{250}{15} \times 3 \\ = Rs . 50 \end{aligned}$

257.

A and B together can complete a work in 3 days. They start together but after 2 days, B left the work. If the work is completed after two more days, B alone could do the work in

(A) 5 days
(B) 6 days
(C) 9 days
(D) 10 days

Solution: 1st Method: (A+B)'s one day's work = $\frac{1}{3}$ part (A+B) works 2 days together = $\frac{2}{3}$ part Remaining work = $1 - \frac{2}{3}$ = $\frac{1}{3}$ part $\frac{1}{3}$ part of work is completed by A in two days Hence, one day's work of A = $\frac{1}{6}$ Then, one day's work of B = $\frac{1}{3} - \frac{1}{6}$ = $\frac{1}{6}$ So, B alone can complete the whole work in 6 days. 2nd Method: (A+B)'s one day's % work = $\frac{100}{3}$ = 33.3% Work completed in 2 days = 66.6% Remaining work = 33.4% One day's % work of A = $\frac{33.4}{2}$ = 16.7% One day's work of B = 33.4 - 16.7 = 16.7% B alone can complete the work in, = $\frac{100}{16.7}$ = 5.98 days ≈ 6 days.

258.

Working efficiencies of P and Q for completing a piece of working are in the ratio 3 : 4. The number of days to be taken by them to complete the work will be in the ratio ?

(A) 3 : 2
(B) 2 : 3
(C) 3 : 4
(D) 4 : 3

Solution: Since we know efficiency and time are inversely proportion to each other. $\begin{aligned} P : Q \\ Efficiency 3 : 4 \\ Time 4 : 3 \end{aligned}$

259.

18 men or 36 boys working 6 hours a day can plough a field in 24 days. In how many days will 24 men and 24 boys working 9 hours a day plough the same field ?

(A) 9 days
(B) 10 days
(C) 6 days
(D) 8 days

Solution: Let the required no of days be x. 18 Men = 36 Boys 1 Man = 2 Boys ∴ 24 Men = 48 Boys According to the question, M1D1H1 = M2D2H2 36 × 24 × 6 = (48 + 24) × x × 9 36 × 24 × 6 = 72 × 9 × x x = $\frac{36 \times 6 \times 24}{72 \times 9}$ x = 8 days

260.

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

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Practice MCQ Questions and Answer on Time and Work

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