Practice MCQ Questions and Answer on Time and Work

31.

A conveyor belt delivers baggage at the rate of 3 tons in 5 minutes and second conveyor belt delivers baggage at the rate of 1 ton in 2 minutes. How much time will it take to get 33 tons of baggage delivered using both the conveyor belts together ?

(A) 25 minutes 30 seconds
(B) 30 minutes
(C) 35 minutes
(D) 45 minutes

Solution: Baggage delivered by first belt in 1 minute $= (\frac{3}{5}) tons$ Baggage delivered by second belt in 1 minute $= (\frac{1}{2}) tons$ Baggage delivered by both belt in 1 minute $\begin{aligned} = (\frac{3}{5} + \frac{1}{2}) tons \\ = \frac{11}{10} tons \\ ∴ Required time \\ = (33 \div \frac{11}{10}) minutes \\ = (33 \times \frac{10}{11}) minutes \\ = 30 minutes \end{aligned}$

32.

Two spinning machines A and B can together produce 300000 metres of cloth in 10 hours. If machine B alone can produce the same amount of cloth in 15 hours. Then how much cloth can machine A produce alone in 10 hours ?

(A) 50000 metres
(B) 100000 metres
(C) 150000 metres
(D) 200000 metres

Solution: Length of cloth produced by A and B in 10 hours $= 300000 metres$ Length of cloth produced by B in 10 hours $\begin{aligned} = (\frac{300000}{15} \times 10) \\ = 200000 metres \end{aligned}$ ∴ Length of cloth produced by A in 10 hours $\begin{aligned} = (300000 - 200000) \\ = 100000 metres \end{aligned}$

33.

Smith and Ajit can complete a task in 12 days and 18 days, respectively. If they work together on the task for 4 days, then the fraction of the task that will be left is:

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

Solution: (Smith + Ajit) × 4 = 4 × 5 = 20 Remaining work = 36 - 20 = 16 Then the fraction of the task that will be left is $= \frac{16}{36} = \frac{4}{9}$

34.

4 men and 10 women were put on a work. They completed $\frac{1}{3}$ of the work in 4 days. After this 2 men and 2 women were increased. They completed $\frac{2}{9}$ more of the work in 2 days. If the remaining work is to be completed in 3 days, then how many more women must be increased ?

(A) 8
(B) 32
(C) 50
(D) 55

Solution: $\begin{aligned} Let 1 man's 1 day's work = x \\ And \\ 1 women's 1 day's work = y \\ Then, \\ \Rightarrow 4 x + 10 y = \frac{1}{3} \times \frac{1}{4} = \frac{1}{12} \\ \Rightarrow 4 x + 10 y = \frac{1}{12} \\ \Rightarrow 2 x + 5 y = \frac{1}{24} . . . . . (i) \\ And, \\ \Rightarrow 6 x + 12 y = \frac{1}{9} \\ \Rightarrow 2 x + 4 y = \frac{1}{27} . . . . . (ii) \end{aligned}$ Subtracting (ii) from (i), we get $\begin{aligned} y = \frac{1}{24} - \frac{1}{27} = \frac{1}{216} \\ Now, \end{aligned}$ Now, (6 men + 12 women)'s 3 day's work $\begin{aligned} = (\frac{1}{9} \times 3) \\ = \frac{1}{3} \\ Work completed \\ = (\frac{1}{3} + \frac{2}{9} + \frac{1}{3}) \\ = \frac{8}{9} \\ ∴ Remainig work \\ = (1 - \frac{8}{9}) \\ = \frac{1}{9} \\ 1 women's 3 day's work \\ = (\frac{1}{216} \times 3) \\ = \frac{1}{72} \end{aligned}$ In 3 day's $\frac{1}{72}$ work is done by 1 women. $\begin{aligned} ∴ In 3 day's \frac{1}{9} work is done by \\ = (72 \times \frac{1}{9}) \\ = 8 women . \end{aligned}$

35.

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

36.

4 mat-weavers can weave 4 mats in 4 days. At the same rate how many mats would be woven by 8 mat-weavers in 8 days ?

(A) 4
(B) 8
(C) 12
(D) 16

Solution: $\begin{aligned} \frac{4_{mat - wevers} \times 4_{days}}{4_{mats}} = \frac{8_{mat - wevers} \times 8_{days}}{N_{mats}} \\ \Leftrightarrow N = 16 mats \end{aligned}$

37.

Working together, Asha and Sudha can complete an assigned task in 20 days. However, if Asha worked alone and completed half the work and then Sudha takes over the task and completes the second half of the task, the task will be completed in 45 days. How long will Asha take to complete the if she worked alone ? Assume that Sudha is more efficient than Asha.

(A) 25 days
(B) 30 days
(C) 60 days
(D) 65 days

Solution: Suppose, Asha takes x days to complete the task alone while Sudha takes y days to complete it alone Since Sudha is more efficient than Asha, we have x > y $\begin{aligned} Asha's 1 day's work = \frac{1}{x} \\ Sudha's 1 day's work = \frac{1}{y} \\ (Asha + Sudha)'s 1 day's work \\ = \frac{1}{x} + \frac{1}{y} \\ = \frac{x + y}{x y} \end{aligned}$ If Asha and Sudha each does half of the work alone, time taken $\begin{aligned} = (\frac{x}{2} + \frac{y}{2}) days \\ = (\frac{x + y}{2}) days . \\ ∴ \frac{x + y}{2} = 45 \\ \Rightarrow x + y = 90 \\ From (i) and (ii), \\ We have : \frac{x y}{20} = 90 or x y = 1800 \\ Now, x y = 1800 and x + y = 90 \\ \Rightarrow x = 60, y = 30 [∵ x > y] \end{aligned}$ Hence, Asha alone will take 60 days to complete the task.

38.

A, B and C can complete a piece of work in 24, 5 and 12 days respectively. Working together, they will complete the same work in ?

(A) $\frac{7}{24} days$
(B) $3 \frac{3}{7} days$
(C) $4 days$
(D) $3 \frac{1}{13} days$

Solution: $\begin{aligned} A's 1 day's work = \frac{1}{24} \\ B's 1 day's work = \frac{1}{5} \\ C's 1 day's work = \frac{1}{12} \\ ∴ (A + B + C)'s 1 day's work \\ = \frac{1}{24} + \frac{1}{5} + \frac{1}{12} \\ L .C .M of 24, 5 and 12 \end{aligned}$ 2 24 - 5 - 12 2 12 - 5 - 6 3 6 - 5 - 3 2 - 5 - 1 $\begin{aligned} 2 \times 2 \times 3 \times 2 \times 5 = 120 \\ = \frac{5 + 24 + 10}{120} \\ = \frac{39}{120} \\ = \frac{13}{40} \end{aligned}$ Time taken by A, B and C to complete the work, working together $\begin{aligned} = \frac{40}{13} \\ = 3 \frac{1}{13} days \end{aligned}$

39.

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

40.

X can do a piece of work in 24 days. When he had worked for 4 days, Y joined him. If complete work was finished in 16 days, Y can alone finish that work in ?

(A) 18 days
(B) 27 days
(C) 36 days
(D) 42 days

Solution: $\begin{aligned} X's 1 day's work = \frac{1}{24} \\ X's 16 day's work = \frac{16}{24} \\ Let, \end{aligned}$ Y alone complete the work in x days $Y's 12 day's work = \frac{12}{x}$ According to the question, Complete work done by X and Y = 1 X's 16 day's work + Y's 12 day's work = 1 $\begin{aligned} \Rightarrow \frac{16}{24} + \frac{12}{x} = 1 \\ \Rightarrow \frac{2}{3} + \frac{12}{x} = 1 \\ \Rightarrow \frac{12}{x} = 1 - \frac{2}{3} = \frac{1}{3} \\ \Rightarrow x = 12 \times 3 \\ \Rightarrow x = 36 days \end{aligned}$

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Practice MCQ Questions and Answer on Time and Work

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