Practice MCQ Questions and Answer on Time and Work

231.

P can complete a work in 12 days working 8 hours a day. Q can complete the same work in 8 days working 10 hours a day. If both P and Q work together, working 8 hours a day, in how many days can they complete the work?

(A) $5 \frac{5}{11}$
(B) $5 \frac{6}{11}$
(C) $6 \frac{5}{11}$
(D) $6 \frac{6}{11}$

Solution: $\begin{aligned} P can complete the work \\ = (12 \times 8) hrs . = 96 hrs . \\ Q can complete the work \\ = (8 \times 10) hrs . = 80 hrs . \\ ∴ P's 1 hour's work = \frac{1}{96} and \\ ∴ Q's 1 hour's work = \frac{1}{80} \\ (P + Q)'s 1 hour's work \\ = \frac{1}{96} + \frac{1}{80} = \frac{11}{480} \\ So, both P and Q will finish the work \\ = \frac{480}{11} hrs . \\ ∴ Number of days of 8 hours each \\ \frac{480}{11} \times \frac{1}{8} = \frac{60}{11} days = 5 \frac{5}{11} days \end{aligned}$

232.

A and B can together do a piece of work it in 6 days and A alone can do it in 9 days. The number of days B will take to do it alone is ?

(A) 18 days
(B) 24 days
(C) 9 days
(D) 12 days

Solution: L.C.M. of Total Work = 36 One day work of A + B = $\frac{36}{6}$ = 6 unit/day One day work of A = $\frac{36}{9}$ = 4 unit/day $\begin{aligned} B's efficiency \\ = 6 - 4 \\ = 2 \\ Time taken by B \\ = \frac{36}{2} \\ = 18 days \end{aligned}$

233.

If two persons, with equal abilities, can do two jobs in two days then 100 persons with equal abilities can do 100 similar jobs in = ?

(A) 100 days
(B) 10 days
(C) 5 days
(D) 2 days

Solution: $\frac{2_{person} \times 2_{days}}{2_{jobs}} = \frac{100 \times D}{10 0_{jobs}}$ (D is number of days required) $\begin{aligned} After solving \\ D = 2 days \end{aligned}$

234.

Dinesh and Rakesh are working on an Assignment, Dinesh takes 6 hours to type 32 pages on a computer, while Rakesh 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 page ?

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

Solution: $\begin{aligned} Dinesh's one hour work \\ = \frac{32}{6} \\ = \frac{16}{3} pages/hour \\ Rakesh's one hour work \\ = \frac{40}{5} \\ = 8 pages/hour \\ Dinesh's and Rakesh's one hour work \\ = \frac{16}{3} + 8 \\ = \frac{40}{3} pages/hour \\ They will finish the work together \\ \frac{Total work}{Efficiency} \\ = \frac{110}{\frac{40}{3}} \\ = 8 \frac{1}{4} \\ = 8 hours, 15 minutes \end{aligned}$

235.

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 $= \frac{60}{13} days$

236.

Three taps A, B and C together can fill an empty cistern in 10 minutes. The tap A alone can fill it in 30 minutes and the tap B alone in 40 minutes. How long will the tap C alone take to fill it?

(A) 16 minutes
(B) 24 minutes
(C) 32 minutes
(D) 40 minutes

Solution: A, B and C together can fill 100% empty tank in 10 minutes Work rate of (A + B + C) = $\frac{100}{10}$ = 10% per minute A alone can fill the tank in 30 minutes Work rate of A = $\frac{100}{30}$ = 3.33% per minute B alone can fill the tank in 40 minutes Work rate of B = $\frac{100}{40}$ = 2.5% Work rate of (A + B) = 3.33 + 2.5 = 5.83% per minute Work rate of C, = Work rate of (A + B + C) - (A + B) = 10 - 5.83 = 4.17% per minute So, C takes = $\frac{100}{4.17}$ ≈ 24 minutes to fill the tank

237.

A can do $\frac{1}{3}$ rd of a work in 5 days and B can do the do $\frac{2}{5}$ th of this work in 10 days. Both A and B, together can do the work in ?

(A) $7 \frac{3}{8} days$
(B) $8 \frac{4}{5} days$
(C) $9 \frac{3}{8} days$
(D) 10 days

Solution: $\begin{aligned} \frac{1}{3} work in 5 days \\ then a complete work in \\ = 5 \times 3 = 15 days \\ B \to \frac{2}{5} work in 10 days \\ then B completes work in \\ = 10 \times \frac{5}{2} = 25 days \end{aligned}$ L.C.M. of Total Work =75 One day work of A = $\frac{75}{15}$ = 5 unit/day One day work of B = $\frac{75}{25}$ = 3 unit/day $\begin{aligned} (A + B) can do work \\ = \frac{75}{8} = 9 \frac{3}{8} days \end{aligned}$

238.

10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?

(A) 3
(B) 5
(C) 7
(D) Cannot be determined

Solution: $\begin{aligned} 1 w o m a n^{'} s 1 d a y^{'} s w o r k = \frac{1}{70} \\ 1 child's 1 day's work = \frac{1}{140} \\ (5 women + 10 children)'s day's work \\ = \frac{5}{70} + \frac{10}{140} = \frac{1}{14} + \frac{1}{14} = \frac{1}{7} \\ ∴ 5 women and 10 chidren will complete \\ the work in 7 days \end{aligned}$

239.

A and B can do a work together in 18 days. A is three time as efficient as B. In how many days can B alone complete the work?

(A) 60 days
(B) 72 days
(C) 54 days
(D) 64 days

Solution: A : B = 3 : 1 Total work = 4 × 18 = 72 unit B = $\frac{72}{1}$ = 72 days

240.

While working 7 hour a day, A alone can complete a piece of work in 6 days and B alone in 8 days. In what time would they complete it together, 8 hour a day?

(A) 3 days
(B) 4 days
(C) 2.1 days
(D) 3.6 days

Solution: A can complete the work in 7 × 6 = 42 hours 1 hour's work of A = $\frac{1}{42}$ B can complete the work in 7 × 8 = 56 hours 1 hour's work of B = $\frac{1}{56}$ (A + B)'s 1 hour's work $\begin{aligned} = \frac{1}{42} + \frac{1}{56} \\ = \frac{4 + 3}{168} \\ = \frac{7}{168} \end{aligned}$ ∴ Time taken by (A + B) working 8 hours daily $\frac{168}{7 \times 8} = 3 days$

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Practice MCQ Questions and Answer on Time and Work

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