Practice MCQ Questions and Answer on Time and Work

221.

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 $\begin{aligned} Efficiency of C \\ = 15 - (9 + 3) \\ = 3 \\ C's amount \\ = \frac{250}{15} \times 3 \\ = Rs . 50 \end{aligned}$

222.

P and Q together can do a work in 12 days. P alone can do the same work in 36 days. In how many days can Q alone complete two-third part of the same work?

(A) 12
(B) 18
(C) 21
(D) 15

Solution: Efficiency of Q = 2 So, required answer = $\frac{36 \times \frac{2}{3}}{2}$ = 12 days

223.

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 $\begin{aligned} ∴ \frac{11}{12} part of wall built by A in \\ = (8 \times \frac{11}{12}) \\ = \frac{22}{3} \\ = 7 \frac{1}{3} day \end{aligned}$

224.

12 men can do a piece of work in 15 days and 20 women can do the same work in 12 days. In how many days can 5 men and 5 women complete the same work ?

(A) $20 \frac{4}{7} days$
(B) $2 \frac{4}{7} days$
(C) $20 \frac{3}{7} days$
(D) 18 days

Solution: 12 man × 15 = 20 women × 12 = Total work 3 man = 4 women $\begin{aligned} \frac{Men}{Women} = \frac{4}{3} \to Efficiency \\ Total work = 12 \times 4 \times 15 = 720 \\ (5 man + 5 women) \times D = 720 \\ D (5 \times 4 + 5 \times 3) = 720 \\ D = \frac{720}{35} = 20 \frac{4}{7} days \end{aligned}$ Alternate: According to the question, 12 men can do the 1 day work in $\frac{1}{15}$ days So, 1 men can do the 1 day work in $\frac{1}{15 \times 12}$ = $\frac{1}{180}$ days 5 men can do the 1 day work in $\frac{1}{180} \times 5$ = $\frac{5}{180}$ days Similarly 5 women do the 1 dys work $\frac{5}{240}$ days ∴ 5 men & 5 women together work in 1 day $\begin{aligned} = \frac{5}{180} + \frac{5}{240} \\ = \frac{20 + 15}{720} \\ = \frac{35}{720} \end{aligned}$ Hence, they complete the work $\frac{720}{35}$ = $20 \frac{4}{35}$ days

225.

To do a certain work, A and B work on alternate days, with B beginning the work on the first day. A can finish the work alone in 48 days. If the work gets completed in $11 \frac{1}{3}$ ÃÂÃÂ days, then B alone can finish 4 times the same work in:

(A) 24 days
(B) 32 days
(C) 27 days
(D) 30 days

Solution: Let total work = 48 unit B × 6 + A × $\frac{16}{3}$ = 48 B × 6 + 1 × $\frac{16}{3}$ = 48 B × 6 = $\frac{128}{3}$ B = $\frac{64}{9}$ 4 × Total work = B × Days Now, 48 × 4 = $\frac{64}{9}$ × Days 27 = Days

226.

If 3 men or 9 boys can finish a piece of work in 21 days, in how many days can 5 men and 6 boys together do the same piece of work ?

(A) 8 days
(B) 12 days
(C) 14 days
(D) Cannot be determined

Solution: Answer & Solution Answer: Option E Solution: $\begin{aligned} 1 men's 1 day's work \\ = \frac{1}{21 \times 3} \\ = \frac{1}{63} \\ 1 boy's 1 day's work \\ = \frac{1}{21 \times 9} \\ = \frac{1}{189} \\ (5 men + 6 boy)'s 1 day's work \\ = \frac{5}{63} + \frac{6}{189} \\ = \frac{5}{63} + \frac{2}{63} \\ = \frac{7}{63} \\ = \frac{1}{9} \end{aligned}$ Hence, 5 men's and 6 boy's together can do the work in 9 days.

227.

If 4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days, then 10 women complete it in ?

(A) 35 days
(B) 50 days
(C) 45 days
(D) 40 days

Solution: $\begin{aligned} According to the question, \\ \Rightarrow 4m + 6w = 8 days . . . . . (i) \\ or \\ \Rightarrow 32m + 48 w = 1 days \\ \Rightarrow 3m + 7 w = 10 days . . . . . (ii) \\ or \\ \Rightarrow 30m + 70 w = 1 day \\ ∴ 32m + 48w = 30 m + 70 w \\ \Rightarrow 2m = 22 w \\ \Rightarrow m = 11 w \\ From (i) \\ \Rightarrow 4m = 44 w \\ ∴ (44w + 6w) \times 8 = 10 w \times x \\ \Rightarrow 50w \times 8 = 10 w \times x \\ \Rightarrow x = 40 days \end{aligned}$

228.

A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?

(A) 8 hours
(B) 10 hours
(C) 12 hours
(D) 24 hours

Solution: $\begin{aligned} A's 1 hour's work = \frac{1}{4}; \\ (B + C)'s 1 hour's work = \frac{1}{3}; \\ (A + C)'s 1 hour's work = \frac{1}{2} . \\ (A + B + C)'s 1 hour's work \\ = \frac{1}{4} + \frac{1}{3} = \frac{7}{12} \\ B's 1 hour's work \\ = \frac{7}{12} - \frac{1}{2} = \frac{1}{12} \\ ∴ B along will take 12 hours to do the work \end{aligned}$

229.

A can do a certain work in 12 days. B is 60% more efficient then A. How many days will B and A together take to do the same job?

(A) $\frac{80}{13} days$
(B) $\frac{70}{13} days$
(C) $\frac{75}{13} days$
(D) $\frac{60}{13} days$

Solution: Time taken by B to complete the work $\begin{aligned} = 12 \times \frac{100}{160} \\ = \frac{15}{2} days \end{aligned}$ ∴ (A + B)'s 1 day's work $\begin{aligned} = \frac{1}{12} + \frac{2}{15} \\ = \frac{5 + 8}{60} \\ = \frac{13}{60} \end{aligned}$ Hence, the work will be completed in $\frac{60}{13}$ days Alternate: Ratio of time, taken by A and B = 160 : 100 = 8 : 5 If A takes 8 days, B takes 5 days. If A takes 12 days, B takes = $\frac{5}{8} \times 12 = \frac{15}{2}$ Time take by A = 12 days Time take by B = 7.5 days L.C.M. of Total Work = 60 Ratio of time, taken by A and B = 8 : 5 Time taken by A and B together to complete the task $= \frac{60}{13} days$

230.

To complete a work, A takes 50% more time than B. If together they take 18 days to complete the work, how much time shall B take to do it?

(A) 30 days
(B) 35 days
(C) 40 days
(D) 45 days

Solution: $\begin{aligned} We have \\ B = \frac{3}{2} \times A \\ \to A = \frac{2}{3} \times B \\ One day's work, \\ \Rightarrow A + B = \frac{1}{18} \\ \Rightarrow \frac{2}{3} \times B + B = \frac{1}{18} \\ \Rightarrow \frac{5}{3} \times B = \frac{1}{18} \\ One day's work of B \\ = \frac{3}{90} \end{aligned}$ B alone can complete the work in $\begin{aligned} = \frac{90}{3} \\ = 30 days \end{aligned}$

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Practice MCQ Questions and Answer on Time and Work

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