Practice MCQ Questions and Answer on Time and Work

71.

A can do piece of work in 15 days. B is 25% more efficient than A, and C is 40% more efficient than B, A and C work together for 3 days and then C leaves. A and B together will complete the remaining work in:

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

Solution: $\begin{matrix} \begin{matrix} A B C \\ 4 : 5 : 7 \\ 5 : 7 \end{matrix} \\ Efficiency \to & \overset{―}{4 : 5 : 7} \end{matrix}$ Total work = 4 × 15 = 60 units (A + C) × 3 + (A + B)x = 60 11 × 3 + 9 × x = 60 33 + 9x = 60 9x = 27 x = 3 days

72.

A, B and C can all together do a piece of work in 10 days, in which B takes 3 times as long as A and C together to do the work. In how many days can B alone do the work?

(A) 50 days
(B) 40 days
(C) 10 days
(D) 15 days

Solution: $\begin{matrix} (A + C) & : & B \\ Time & 1 & 3 \\ Efficiency & 3 & 1 \end{matrix}$ $B alone = \frac{10 \times 4}{1} = 40 days$

73.

A can complete a certain work in 35 days and B can complete the same work in 15 days. They worked together for 7 days, then B left the work. In how many days will A alone complete 60% of the remaining work?

(A) 7
(B) 15
(C) 10
(D) 8

Solution: 7 days work of (A and B) = 7 × 10 = 70 Remaining work = 105 - 70 = 35 60% of remaining work done by A = $\frac{35 \times \frac{3}{5}}{3}$ = 7 days

74.

Subhash can copy 50 pages in 10 hours; Subhash and Prakash together can copy 300 pages in 40 hours. In how much time can Prakash copy 30 pages?

(A) 13 hour
(B) 12 hour
(C) 11 hour
(D) 9 hour

Solution: Number of page copied by (Subhash + Prakash) in 1 hour = $\frac{300}{40}$ = 7.5 pages; Subhash copied pages in one hour = $\frac{50}{10}$ = 5 pages Hence, Prakash copied pages in one hour = 7.5 - 5 = 2.5 Thus, Prakash can copied 30 pages in = $\frac{30}{2.5}$ = 12 hour

75.

A is twice as efficient as B, and they take equal time as the time taken by C and D to do this work together. If C and D can complete the same work in 15 and 20 days respectively, then. In how many days can A alone complete the work?

(A) $\frac{85}{7}$
(B) $\frac{90}{7}$
(C) $\frac{77}{4}$
(D) $\frac{65}{4}$

Solution: A = 2B B = $\frac{A}{2}$ Efficiency of (A + B) = Efficiency of (C + D) $\begin{aligned} A + B = 7 \\ \Rightarrow A + \frac{A}{2} = 7 \\ \Rightarrow A = \frac{14}{3} \\ Time of A = \frac{60 \times 3}{14} = \frac{90}{7} Answer \end{aligned}$

76.

A and B can complete a piece of work in 12 and 18 days respectively. A begins to do the work and they work alternatively one at a time for one day each. The whole work will be complete in ?

(A) $14 \frac{1}{3} days$
(B) $15 \frac{1}{3} days$
(C) $16 \frac{1}{3} days$
(D) $18 \frac{2}{3} days$

Solution: A's one day work = 3 units B's one day work = 2 units A starts the work and does 3 units and B does the work 2 units/day. They both do 5 units of work in 2 days. They both do 35 units of work in 14 days (Divide $\frac{36}{5}$ , take it to the closest) $\begin{aligned} Work left \Rightarrow 36 - 35 = 1 unit . \\ Now, A's turn . \\ A completes \\ \Rightarrow \frac{1 unit}{3 units/day} \\ = \frac{1}{3} day \\ Whole work completes in \\ \Rightarrow 14 + \frac{1}{3} \\ = 14 \frac{1}{3} days \end{aligned}$

77.

A can complete a certain work in 4 minutes, B in 5 minutes, C in 6 minutes, D in 10 minutes and E in 12 minutes. The average number of units of work completed by them per minute will be = ?

(A) 0.16
(B) 0.40
(C) 0.80
(D) None of these

Solution: $\begin{aligned} Required average, \\ = \frac{\frac{1}{4} + \frac{1}{5} + \frac{1}{6} + \frac{1}{10} + \frac{1}{12}}{5} \\ = \frac{48}{60} \times \frac{1}{5} \\ = \frac{4}{25} \\ = 0.16 \end{aligned}$

78.

A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days?

(A) 11 days
(B) 13 days
(C) $20 \frac{3}{17}$ days
(D) None of these

Solution: $\begin{aligned} Ratio of times taken by A and B \\ = 100 : 130 = 10 : 13 \\ Suppose B takes x days to do the work \\ Then, 10 : 13 :: 23 : x \\ \Rightarrow x = \frac{23 \times 13}{10} \\ \Rightarrow x = \frac{299}{10} \\ A's 1 day's work = \frac{1}{23} \\ B's 1 day's work = \frac{10}{299} \\ (A + B)'s 1 day's work \\ = \frac{1}{23} + \frac{10}{299} \\ = \frac{23}{299} \\ = \frac{1}{13} \\ ∴ A and B together can complete \\ the work in 13 days . \end{aligned}$

79.

18 men can complete a piece of work in 63 days. 9 women take 189 days to complete the same piece of work. How many days will 4 men, 9 women and 12 children together take to complete the piece of work if 7 children alone can complete the piece of work in 486 days ?

(A) 54 days
(B) 63 days
(C) 76 days
(D) 81 days

Solution: $\begin{aligned} 1 men's 1 day's work \\ = \frac{1}{63 \times 18} \\ = \frac{1}{1134} \\ 1 women's 1 day's work \\ = \frac{1}{189 \times 9} \\ = \frac{1}{1701} \\ 1 children's 1 day's work \\ = \frac{1}{486 \times 7} \\ = \frac{1}{3402} \end{aligned}$ (4 men + 9 women + 12 children)'s 1 day's work $\begin{aligned} = \frac{4}{1134} + \frac{9}{1701} + \frac{12}{3402} \\ = \frac{42}{3402} \\ = \frac{1}{81} \end{aligned}$ Hence, 4 mens , 9 women and 12 children together will complete the work in 81 days.

80.

5 men and 2 women working together can do four times as much work per hour as a men and a women together. The work done by a men and a women should be in the ratio ?

(A) 1 : 2
(B) 2 : 1
(C) 1 : 3
(D) 4 : 1

Solution: $\frac{5 men + 2 women}{4 work}$ = $(1 men + 1 women)$ $5 men + 2 women$ = $4 men + 4 women$ $\begin{aligned} 1 men = 2 women \\ \frac{Men}{Women} = \frac{2}{1} \\ M : W \\ 2 : 1 \end{aligned}$

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Practice MCQ Questions and Answer on Time and Work

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