Practice MCQ Questions and Answer on Time and Work

91.

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

92.

A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone?

(A) 30 days
(B) 40 days
(C) 60 days
(D) 70 days

Solution: $\begin{aligned} Let A's 1 day's work = x and \\ B's 1 day's work = y \\ Then, x + y = \frac{1}{30} \\ 16 x + 44 y = 1 \\ Solving these two equations, we get \\ x = \frac{1}{60} and y = \frac{1}{60} \\ ∴ B's 1 day's work = \frac{1}{60} \\ Hence, B alone shall finish the \\ whole work in 60 days \end{aligned}$

93.

A and B can do a job together in 7 days. A is $1 \frac{3}{4}$ ÃÂÃÂ times as efficient as B. The same job can be done by A alone in :

(A) $9 \frac{1}{3}$ days
(B) 11 days
(C) $12 \frac{1}{4}$ days
(D) $16 \frac{1}{3}$ days

Solution: $\begin{aligned} (A's 1 day's work) : (B's 1 day's work) \\ = \frac{7}{4} : 1 = 7 : 4 \\ Let A's and B's 1 day's work be \\ 7 x and 4 x respectively \\ Then, 7 x + 4 x = \frac{1}{7} \\ \Rightarrow 11 x = \frac{1}{7} \\ \Rightarrow x = \frac{1}{77} \\ ∴ A's 1 day's work \\ = \frac{1}{77} \times 7 = \frac{1}{11} \end{aligned}$ So, A will do the work in 11 days

94.

P is thrice as good a workman as Q and therefore able to finish a job in 48 days less than Q. Working together, they can do it in ?

(A) 18 days
(B) 24 days
(C) 30 days
(D) 12 days

Solution: Let time taken by P = x days Then, time taken by Q = 3x days ∴ 3x - x = 48 ⇒ 2x = 48 ⇒ x = 24 ∴ (P + Q)'s 1 day's work $\begin{aligned} = \frac{1}{24} + \frac{2}{72} \\ = \frac{3 + 1}{72} \\ = \frac{1}{18} \end{aligned}$ ∴ Required time = 18 days Alternate: Ratio of times taken by P and Q = 1 : 3 The time difference is 3 - 1 = 2 days while Q take 3 days and P takes 1 day If difference of time is 2 days, Q takes 3 days If difference of time is 48 days, $\begin{aligned} Q takes = (\frac{3}{2} \times 48) \\ = 72 days \end{aligned}$ So, P takes 24 days to do the work. $\begin{aligned} P's 1 day's work = \frac{1}{24} \\ Q's 1 day's work = \frac{1}{72} \\ (P + Q)'s 1 day's work \\ = (\frac{1}{24} + \frac{1}{72}) = \frac{4}{72} = \frac{1}{18} \end{aligned}$ ∴ A and B together can do the work in $\frac{18}{1} = 18 days$

95.

A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work?

(A) 18 days
(B) 24 days
(C) 30 days
(D) 36 days

Solution: $\begin{aligned} 2(A + B + C)'s 1 day's work \\ = \frac{1}{30} + \frac{1}{24} + \frac{1}{20} \\ = \frac{15}{120} = \frac{1}{8} \\ ∴ (A + B + C)'s 1 day's work \\ = \frac{1}{2 \times 8} = \frac{1}{16} \\ Work done by A, B, C in 10 days \\ = \frac{10}{16} = \frac{5}{8} \\ Remaining work \\ = 1 - \frac{5}{8} = \frac{3}{8} \\ A's 1 day's work \\ = \frac{1}{16} - \frac{1}{24} = \frac{1}{48} \\ Now, \frac{1}{48} work isdone by A in 1 day \\ So, \frac{3}{8} work will be done by A in \\ 48 \times \frac{3}{8} = 18 days \end{aligned}$

96.

A can complete a piece of work in 18 days, B in 20 days and C in 30 days, B and C together start the work and forced to leave after 2 days. The time taken by A alone to complete the remaining work is:

(A) 10 days
(B) 12 days
(C) 15 days
(D) 16 days

Solution: 1st Method: $\begin{aligned} (B + C) 2 days work \\ = 2 \times (\frac{1}{20} + \frac{1}{30}) \\ = 2 \times \frac{3 + 2}{60} \\ = \frac{1}{6} part \\ Remaining work \\ = 1 - \frac{1}{6} \\ = \frac{5}{6} part \\ A's one day's work \\ = \frac{1}{18} part \\ Time taken to complete the work \\ = \frac{\frac{5}{6}}{\frac{1}{18}} days \\ Hence, \\ Time taken to complete the work \\ = \frac{5}{6} \times 18 \\ = 15 days \end{aligned}$ 2nd Method: % of work B completes in one day = $\frac{100}{20}$ = 5%; % of work C completes in one day = $\frac{100}{30}$ = 3.33%; % of work (A + B) completes together in one day = 5 + 3.33 = 8.33%; % work (A + B) completes together in 2 days = 8.66 × 2 = 16.66%; Remaining work = 100 - 16.66 = 83.34%; % of work A completes in 1 day = $\frac{100}{18}$ = 5.55% Time taken to complete the remaining work by A = $\frac{83.34}{5.55}$ = 15 days

97.

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

98.

If there is a reduction in the number of workers in a factory in the ratio 15 : 11 and an increment in their wages in the rate 22 : 25, then the ratio by which the total wages of the workers should be decreased is = ?

(A) 6 : 5
(B) 5 : 6
(C) 3 : 7
(D) 3 : 5

99.

Ronald and Elan are working on an assignment. Ronald takes 6 hours to type 32 pages on a computer, while Elan takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages ?

(A) 7 hours 30 minutes
(B) 8 hours
(C) 8 hours 15 minutes
(D) 8 hours 25 minutes

Solution: Number of pages typed by Ronald in 1 hour $\begin{aligned} = \frac{32}{6} \\ = \frac{16}{3} \end{aligned}$ Number of pages typed by Elan in 1 hour $\begin{aligned} = \frac{40}{5} \\ = 8 \end{aligned}$ Number of pages typed by both in 1 hour $\begin{aligned} = (\frac{16}{3} + 8) \\ = \frac{40}{3} \end{aligned}$ ∴Time taken by both to type 110 pages $\begin{aligned} = (100 \times \frac{3}{40}) hours \\ = 8 \frac{1}{4} hours \\ = 8 hours 15 minutes \end{aligned}$

100.

A completes $\frac{7}{10}$ of the work 15 days. Then he completes the remaining work the help of B in 4 days. The time required for A and B together to complete the entire work is = ?

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

Solution: $\begin{aligned} (A + B)'s 4 day's work \\ = (1 - \frac{7}{10}) \\ = \frac{3}{10} \\ (A + B)'s 1 day's work \\ = (\frac{3}{10} \times \frac{1}{4}) \\ = \frac{3}{40} \\ Remaining work \\ = (1 - \frac{3}{10}) \\ = \frac{7}{10} \\ (B + C)'s 1 day's work \\ = (\frac{1}{15} + \frac{1}{20}) \\ = \frac{7}{60} \end{aligned}$ Hence, A an B together take $= \frac{40}{3} = 13 \frac{1}{2}$ days to complete the entire work.

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Practice MCQ Questions and Answer on Time and Work

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