Practice MCQ Questions and Answer on Time and Work

291.

A and B working together completed a job in 5 days. If A works twice as efficiently as he actually did and B works $\frac{1}{3}$ of actual efficiency, the work would have completed in 3 days. Find the for A to complete the job alone.

(A) $6 \frac{1}{2}$
(B) $6 \frac{1}{4}$
(C) $6 \frac{3}{4}$
(D) $12 \frac{1}{2}$

Solution: One Day's work of A and B together, $\frac{1}{A} + \frac{1}{B} = \frac{1}{5} . . . . . . . . (i)$ When A works with twice efficiency,Then, $\frac{2}{A} + \frac{1}{3 B} = \frac{1}{3} . . . . . . . . (ii)$ on solving equations (i) and (ii), we get $A = \frac{25}{4} = 6 \frac{1}{4}$

292.

A can complete $\frac{1}{3}$ of a work in 5 days and B, $\frac{2}{5}$ of the work in 10 days. In how many days both A and B together can complete the work ?

(A) $7 \frac{1}{2}$
(B) $8 \frac{4}{5}$
(C) $9 \frac{3}{8}$
(D) 10

Solution: Whole work will be done by A in $\begin{aligned} = (5 \times 3) \\ = 15 days \end{aligned}$ Whole work will be done by B in $\begin{aligned} = (10 \times \frac{5}{2}) \\ = 25 days \end{aligned}$ $\begin{aligned} A's 1 day's work = \frac{1}{15} \\ B's 1 day's work = \frac{1}{25} \\ (A + B)'s 1 day's work \\ = (\frac{1}{15} + \frac{1}{25}) \\ = \frac{16}{150} \\ = \frac{8}{75} \end{aligned}$ ∴ A and B together can complete the work in $\begin{aligned} = \frac{75}{8} \\ = 9 \frac{3}{8} days . \end{aligned}$

293.

A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?

(A) 5
(B) $5 \frac{1}{2}$
(C) 6
(D) 8

Solution: $\begin{aligned} B's 10 day's work \\ = \frac{1}{15} \times 10 = \frac{2}{3} \\ Remaining work \\ = 1 - \frac{2}{3} = \frac{1}{3} \\ Now, \frac{1}{18} work is done by A in 1 day \\ ∴ \frac{1}{3} work is done by A in \\ 18 \times \frac{1}{3} = 6 days \end{aligned}$

294.

A and B together can do a piece of work in 30 days, B and C together can do it in 20 days, A starts the work and works on it for 5 days, B takes up and work for 15 days. Finally C finishes the work in 18 days. The number of days in which C alone can do the work where doing it separately is = ?

(A) 120 days
(B) 40 days
(C) 60 days
(D) 24 days

Solution: L.C.M. of Total Work =60 One day work of A + B = $\frac{60}{30}$ = 2 unit/day One day work of B + C = $\frac{60}{20}$ = 3 unit/day $\begin{aligned} According to the question, \\ \Rightarrow (A + B) . . . . . 30 days \\ \Rightarrow (B + C .) . . . . . 20 days \\ \Rightarrow A . . . . . 5 \\ \Rightarrow B . . . . . 5 + 10 \\ \Rightarrow C . . . . . 10 + 8 days \end{aligned}$ Work done by (A +B) in 5 days = 2 × 5 = 10 units ⇒ Work done by (B + C) in 10 days = 10 × 3 = 30 units ⇒ Total work (finished till now).....40 units ⇒ Remaining work = 60 - 40 = 20 units ⇒ Here we find that C does remaining 20 units in 8 days ⇒ C's efficiency = $\frac{Work}{Day}$ $= \frac{20 Work}{8 Days} = \frac{5}{2}$ ⇒ Therefore, time taken by C alone to complete the work $= \frac{60}{5} \times 2 = 24 days$

295.

Janardan completes $\frac{2}{3}$ of his work in 10 days. Time he will take to complete of the same $\frac{3}{5}$ work, is ?

(A) 4 days
(B) 8 days
(C) 6 days
(D) 9 days

Solution: Janardan completes $\frac{2}{3}$ of work in 10 days Janardan completes 1 of work in $\begin{aligned} = \frac{10 \times 3}{2} \\ = 15 days \end{aligned}$ Janardan completes $\frac{3}{5}$ of work in $\begin{aligned} = 15 \times \frac{3}{5} \\ = 9 days \end{aligned}$

296.

Amit, Bhawana and Chandan can do a piece of work, working together in one day only. Amit is 5 times efficient than Bhawna and Chandan takes half of the number of days taken by Bhawna to do the same work. What is the difference between the number of days taken by Amit and Chandan when they work alone ?

(A) 4
(B) 5
(C) 3
(D) $2 \frac{2}{5}$

Solution: Amit Bhawana Chandan Eff. → 5x x 2x $\begin{aligned} Let total work = 1 \\ Efficiency of (A + B + C) = 1 \\ Then, \\ \Leftrightarrow 5 x + x + 2 x = 1 \\ \Leftrightarrow x = \frac{1}{8} \\ Days taken by Amit \\ = \frac{1}{\frac{5}{8}} \Rightarrow \frac{8}{5} \\ Days taken by Chandan \\ = \frac{1}{\frac{2}{8}} \Rightarrow 4 \\ Difference of days \\ = 4 - \frac{8}{5} \Rightarrow \frac{20 - 8}{5} \Rightarrow 2 \frac{2}{5} \end{aligned}$

297.

12 men can do a piece of work in 24 days. How many days are needed to complete the work, if 8 men do this work ?

(A) 28 days
(B) 36 days
(C) 48 days
(D) 52 days

Solution: 12 men can do a piece of work in 24 days $\Rightarrow M_{1} = 12 and D_{1} = 24$ 8 men can do this work in $D_{2}$ days $\begin{aligned} \Rightarrow M_{2} = 8 \\ M_{1} D_{1} = M_{2} D_{2} \\ \Rightarrow 12 \times 24 = 8 \times D_{2} \\ \Rightarrow D_{2} = \frac{12 \times 24}{8} \\ \Rightarrow D_{2} = 36 days \end{aligned}$

298.

A and B undertake a contract of a task for Rs. 10,800. A and B can complete the task in 45 days and 60 days, respectively. However, to finish the work early, they take C's help and complete the entire work in 20 days. What is the value (in Rs.) of (a - b + 2c), where a, b and c are the shares of A, B and C, respectively, for their contribution to complete the task?

(A) 3000
(B) 6000
(C) 4000
(D) 8000

299.

A certain number of persons can complete a work in 34 days working 9 h a day. If the number of persons is decreased by 40%. Then how many hours a day should the remaining persons work to complete the work in 51 days?

(A) 9
(B) 10
(C) 8
(D) 12

Solution: $40 % \to \frac{- 2}{5} \begin{matrix} \to Men \end{matrix}$ $\begin{aligned} 9 \times 34 \times 5 = 3 \times 51 \times x \\ x = 10 hours \end{aligned}$

300.

A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?

(A) Rs. 375
(B) Rs. 400
(C) Rs. 600
(D) Rs. 800

Solution: $\begin{aligned} C's 1 day's work \\ = \frac{1}{3} - (\frac{1}{6} + \frac{1}{8}) \\ = \frac{1}{3} - \frac{7}{24} \\ = \frac{1}{24} \\ A's wages:B's wages:C's wages \\ = \frac{1}{6} : \frac{1}{8} : \frac{1}{24} \\ = 4 : 3 : 1 \\ ∴ C's share (for 3 days) \\ = R s . (3 \times \frac{1}{24} \times 3200) \\ = R s . 400 \end{aligned}$

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Practice MCQ Questions and Answer on Time and Work

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