Practice MCQ Questions and Answer on Time and Work

241.

A can do three times the work done by B in one day. They together finish $\frac{2}{5}$ of the work in 9 days. The number of days by which B can do the work alone are ?

(A) 120 days
(B) 100 days
(C) 30 days
(D) 90 days

Solution: Efficiency of A = 3 efficiency of B $(A = 3, B = 1)$ $\frac{2}{5}$ th of the work done by (A + B) in 9 days Total work (A + B) = $\frac{45}{2}$ days will be completed $\begin{aligned} Total work \\ = days \times efficiency (A + B) \\ = \frac{45}{2} \times 4 \\ = 90 \\ Number of days for B \\ = \frac{Total work}{Efficiency} \\ = \frac{90}{1} \\ = 90 days \end{aligned}$

242.

A man and a boy received Rs. 800 as wages for 5 days for the work they did together. The man's efficiency in the work was thrice times that of the boy. What are the daily wages of the boy?

(A) Rs. 76
(B) Rs. 56
(C) Rs. 44
(D) Rs. 40

Solution: Man = 3 boy Daily wages for them = $\frac{800}{5}$ = 160 4 boy (1 man + 1 boy) = 160 4 boy = 160 Or, boy = Rs. 40

243.

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

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

244.

A and B together can do a piece of work in 8 days, B and C together in 10 days, while C and A together in 6 days, if they all work together the work will be completed in ?

(A) $3 \frac{3}{4} days$
(B) $3 \frac{3}{7} days$
(C) $5 \frac{5}{47} days$
(D) $4 \frac{4}{9} days$

Solution: In these kind of questions, always take total work as L.C.M. of number of days Here L.C.M. of Total Work = 120 One day work of A + B = $\frac{120}{8}$ = 15 unit/day One day work of B + C = $\frac{120}{10}$ = 12 unit/day One day work of C + A = $\frac{120}{6}$ = 20 unit/day ∴ Total units per day = 15 + 12 + 20 = 47 ∴ Efficiency of : $\begin{aligned} 2 (A + B + C) = 47 \\ A + B + C = \frac{47}{2} \end{aligned}$ (A + B + C) will complete the whole work in $\begin{aligned} = \frac{120}{\frac{47}{2}} \\ = \frac{240}{47} \\ = 5 \frac{5}{47} days \end{aligned}$

245.

A and B can together finish a piece of work in 30 days. They worked on it 20 days and then B left. The remaining work was done by A alone in 20 days. A alone can finish the work in = ?

(A) 60 days
(B) 54 days
(C) 48 days
(D) 50 days

Solution: (T.W.)60 2 units/day ↓ 30 days(A + B) $\begin{aligned} (A + B) worked for 20 days \\ So, they completed \\ 20 \times 2 = 40 units \\ Work left = 60 - 40 = 20 units \end{aligned}$ (T.W.) 2 0 1 units/day ↓ 20 days (A) A's efficiency 1 units/day A will complete the whole work in $\begin{aligned} = \frac{Total work}{Efficiency} \\ = \frac{60}{1} \\ = 60 days \\ A l t e r n a t e : \\ (A + B) \times 10 = A \times 20 \\ \frac{A + B}{A} = \frac{2}{1} \\ Total work \\ = 2 \times 30 \\ = 60 units \\ Time taken by A alone \\ = \frac{60}{1} \\ = 60 days \end{aligned}$

246.

A tyre has 3 punctures. The first puncture alone would have made the tyre flat in 9 minutes, the second alone would have done it in 18 minutes, the third alone would have done it in 6 minutes. If the air leaks out at a constant rate, then how long (in minutes) does it take for all the punctures together to make it flat?

(A) 2
(B) 6
(C) 4
(D) 3

Solution: $∴ \frac{18}{2 + 1 + 3} = 3 minutes$

247.

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

248.

Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is:

(A) 15
(B) 16
(C) 18
(D) 25

Solution: Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4 Suppose Tanya takes x days to do the work 5 : 4 :: 20 : x ⇒ $x = \frac{4 \times 20}{5}$ ⇒ x = 16 days Hence, Tanya takes 16 days to complete the work

249.

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 $\begin{aligned} A l t e r n a t e : \\ (2 m + 3w) \times 20 = 4m \times 20 \\ \frac{m}{w} = \frac{3}{2} \\ Total work \\ = (2 \times 3 + 3 \times 2) \times 20 \\ = 240 units \\ 5 men efficiency \\ = 5 \times 3 \\ = 15 \\ Required number of days \\ = \frac{240}{15} \\ = 16 days \end{aligned}$

250.

If 12 carpenters working 6 hours a day can make 460 chairs in 240 days, then number of chairs made by 18 carpenters in 360 days each working 8 hours a day ?

(A) 1320
(B) 1380
(C) 1260
(D) 920

Solution: $According to the question,$ $\Rightarrow \frac{12 \times 6 \times 240}{460}$ = $\frac{18 \times 360 \times 8}{x}$ $\begin{aligned} \Rightarrow x = \frac{18 \times 360 \times 8 \times 460}{12 \times 6 \times 240} \\ \Rightarrow x = 1380 \end{aligned}$

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Practice MCQ Questions and Answer on Time and Work

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