Practice MCQ Questions and Answer on Time and Work

41.

A is 40% more efficient than B and C is 20% less efficient than B. Working together, they can finish a task in 15 days. In how many days, will B alone complete 75% of the task?

(A) 36
(B) 48
(C) 32
(D) 44

Solution: $\begin{aligned} (7 + 5 + 4) \times 15 \times \frac{75}{100} = B \times 5 \\ B = 36 days \end{aligned}$

42.

40 men can complete a piece of work in 15 days. 20 more men joined them after 5 days they start doing work. How many days will be required by them to finish the remaining work ?

(A) $7 \frac{2}{3} days$
(B) $6 \frac{1}{5} days$
(C) $8 \frac{1}{4} days$
(D) $6 \frac{2}{3} days$

Solution: Work done by 40 men in 5 days = $\frac{1}{3}$ (As if whole work is completed in 15 days then in 5 days ${\frac{1}{3}}^{rd}$ of the work will be finished) $\begin{aligned} Remaining work = 1 - \frac{1}{3} = \frac{2}{3} \\ ∵ 40 men do 1 work in 15 days . \\ 60 men can do \frac{2}{3} work in x day \\ \frac{M_{1} D_{1}}{W_{1}} = \frac{M_{2} D_{2}}{W_{2}} \\ M_{1} = 40, M_{2} = 60 \\ D_{1} = 15, D_{2} = x \\ W_{1} = 1, W_{2} = \frac{2}{3} \\ \Rightarrow \frac{40 \times 15}{1} = \frac{60 \times x}{2} \\ \Rightarrow \frac{2}{3} (40 \times 15) = 60 x \\ \Rightarrow 2 \times 40 \times 5 = 60 x \\ \Rightarrow x = \frac{20}{3} \\ \Rightarrow x = 6 \frac{2}{3} days \end{aligned}$

43.

X can do a piece of work in 24 days. When he had worked for 4 days, Y joined him. If complete work was finished in 16 days, Y can alone finish that work in:

(A) 27 days
(B) 36 days
(C) 42 days
(D) 18 days

Solution: According to the question, X → 24 days ⇒ Work done by X in 4 days alone = 4 × 1 = 4 units ⇒ Remaining work = 24 - 4 = 20 units ⇒ 20 units done by both together in (16 - 4 days) = 12 days ⇒ Then efficiencies of (X + Y) $= \frac{work}{days} = \frac{20}{12} = \frac{5}{3} = 1 + \frac{2}{3}$ ⇒ Efficiency of Y = $\frac{2}{3}$ ⇒ Time taken by Y alone to complete the total work $= \frac{24}{\frac{2}{3}} = 36 days$ Alternate solution: $\begin{aligned} X \times 20 = (X + Y) \times 12 \\ \frac{X}{X + Y} = \frac{12}{20} \\ = \frac{3 \to Efficiency of X}{5 \to Efficiency of (X + Y)} \end{aligned}$ Efficiency of Y = 5 - 3 = 2 units/day Total work = 24 × 3 = 72 units Total time taken by Y = $\frac{72}{2}$ = 36 days

44.

Twenty women together can complete a piece of work in 16 days, 16 men together can complete the same work in 15 days. The ratio of the working capacity of a man to that of a women is = ?

(A) 3 : 4
(B) 4 : 3
(C) 5 : 3
(D) 4 : 5

Solution: $\begin{aligned} 20 w \times 16 = 16 m \times 15 \\ 20 w = 15 m \\ 4 w = 3 m \\ \frac{m}{w} = \frac{4}{3} \\ ∴ Man : Women \\ 4 : 3 \end{aligned}$

45.

A can build up a wall in 8 days while B can break it in 3 days. A has worked for 4 days and then B joined to work with A for another 2 days only. In how many days will A alone build up the remaining part of the wall ?

(A) $6 \frac{1}{3} days$
(B) 7 days
(C) $7 \frac{1}{3} days$
(D) $13 \frac{1}{3} days$

Solution: Part of wall built by A in 1 day = $\frac{1}{8}$ Part of wall broken by B in 1 day = $\frac{1}{3}$ Part of wall built by A in 4 days $\begin{aligned} = (\frac{1}{8} \times 4) \\ = \frac{1}{2} \end{aligned}$ Part of wall broken by B and built by A in 2 days $\begin{aligned} = 2 (\frac{1}{3} - \frac{1}{8}) \\ = \frac{5}{12} \end{aligned}$ $\begin{aligned} Part of wall built in 6 days \\ = (\frac{1}{2} - \frac{5}{12}) \\ = \frac{1}{12} \\ Remaining part to be built \\ = (1 - \frac{1}{12}) \\ = \frac{11}{12} \end{aligned}$ Now, $\frac{1}{8}$ part of wall built by A in 1 day $\begin{aligned} ∴ \frac{11}{12} part of wall built by A in \\ = (8 \times \frac{11}{12}) \\ = \frac{22}{3} \\ = 7 \frac{1}{3} day \end{aligned}$

46.

12 monkeys can eat 12 bananas in 12 minutes. In how many minutes can 4 monkeys eat 4 bananas ?

(A) 4 minutes
(B) 10 minutes
(C) 12 minutes
(D) 8 minutes

Solution: $\begin{aligned} Let the required time = T \\ \Rightarrow \frac{m_{1} \times d_{1} \times t_{1}}{w_{1}} = \frac{m_{2} \times d_{2} \times t_{2}}{w_{2}} \\ \Rightarrow \frac{12 \times 12}{12} = \frac{4 \times time}{4} \\ \Rightarrow Time = 12 minutes \end{aligned}$

47.

A can do a piece of work in 18 days. He worked at it for 12 days and B finished the remaining work in 8 days. B alone can do the whole work in ?

(A) 16 days
(B) 24 days
(C) 35 days
(D) 28 days

Solution: $\begin{aligned} 18A = 12A + 8B \\ 6A = 8B \\ \frac{A}{B} = \frac{4}{3} \\ So, \\ Efficiency of A and B are 4, 3. \\ Total work \\ = 18 \times 4 \\ = 72 units \\ So, B will do \\ = \frac{72}{3} \\ = 24 days \end{aligned}$

48.

A, B and C completed a work costing Rs. 1800. A worked for 6 days, B for 4 days and C for 9 days. If their daily wages are in the ratio of 5 : 6 : 4, how much amount will be received by A ?

(A) Rs. 600
(B) Rs. 750
(C) Rs. 800
(D) Rs. 900

Solution: Let the daily wages of A, B and C be Rs. 5x, Rs. 6x and Rs. 4x respectively. Then, ratio of their amounts $\begin{aligned} = (5 x \times 6) : (6 x \times 4) : (4 x : 9) \\ = 30 : 24 : 36 \\ = 5 : 4 : 6 \\ ∴ A's amount \\ = Rs . (1800 \times \frac{5}{15}) \\ = Rs .600 \end{aligned}$

49.

If 10 men or 20 boys can make 260 mats in 20 days, then how many mats will be made by 8 men and 4 boys in 20 days?

(A) 260
(B) 240
(C) 280
(D) 520

50.

16 men can finish a work in 24 days and 48 boys can finish the same work in 16 days. 12 men started the work and after 4 days 12 boys joined them. In how many days can they finish the remaining work ?

(A) 6
(B) 12
(C) 16
(D) None of these

Solution: $\begin{aligned} 1 men's 1 day's work \\ = \frac{1}{24 \times 16} \\ = \frac{1}{384} \\ 1 boy's 1 day's work \\ = \frac{1}{16 \times 48} \\ = \frac{1}{768} \\ 12 men's 4 day's work \\ = (\frac{12}{384} \times 4) \\ = \frac{1}{8} \\ Remaining work \\ = (1 - \frac{1}{8}) \\ = \frac{7}{8} \\ (12 men + 12 boy)'s 1 day's work \\ = (\frac{12}{384} + \frac{12}{768}) \\ = (\frac{1}{32} + \frac{1}{64}) \\ = \frac{3}{64} \end{aligned}$ $\frac{3}{64}$ work is done by (12 men + 12 boy)'s in 1 day $\begin{aligned} ∴ \frac{7}{8} work is done by them in \\ = \frac{64}{3} \times \frac{7}{8} days \\ = \frac{56}{3} days \\ = 18 \frac{2}{3} days \end{aligned}$

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Practice MCQ Questions and Answer on Time and Work

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