Practice MCQ Questions and Answer on Time and Work

11.

Vijay can chop all the vegetables available in 4 minutes lesser time than Bishaka. If both of them work together, they take 288 seconds to chop all the vegetables. How long does Vijay alone take to chop all the vegetables?

(A) 7 min
(B) 9 min
(C) 8 min
(D) 6 min

Solution: By the option ⇒ $\frac{24}{5}$ = 4.8 minutes = 288 seconds (satisfied)

12.

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

13.

A can do $\frac{1}{3}$ of a work in 30 days, B can do $\frac{2}{5}$ of the same work in 24 days. They worked together for 20 days. C complete the remaining work in 8 days. Working together A, B and C will complete the same work in:

(A) 15 days
(B) 10 days
(C) 18 days
(D) 12 days

Solution: ⇒ A can do $\frac{1}{3}$ of a work in 30 day ⇒ A completed work in 90 days ⇒ B can do $\frac{2}{5}$ of the same work in 24 days ⇒ B can completed work in 60 days ⇒ Let the total work = LCM (90, 60) = 180 unit ⇒ Efficiency of A = 3 unit/day ⇒ Efficiency of B = 2 unit/day ⇒ They both worked for 20 days, work done in 20 days = 20 × 5 = 100 unit ⇒ Remaining work = 180 - 100 = 80 unit ⇒ Remaining work done by C in 8 days ⇒ Efficiency of C = 10 unit/day ⇒ Efficiency of (A + B + C) = 15 unit/day ⇒ Work completed = $\frac{180}{15}$ = 12 days ∴ If all worked together, the work complete in 12 days.

14.

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

15.

A can do a work in 36 days, B in 18 days and C in 12 days. Every 2nd day B and every 3rd day C, helps A .Then in how many days the work will be completed?

(A) 12
(B) 14
(C) 10
(D) 8

Solution: Let to work Total Work = 36 One day work of A = $\frac{36}{36}$ = 1 unit/day One day work of B = $\frac{36}{18}$ = 2 unit/day One day work of C = $\frac{36}{12}$ = 3 unit/day In 3 days cycle total work done is A, A + B, A + C = 1 + (1 + 2) + (1 + 3) = 8 unit/Cycle ∴ 32 units of the work completed in 4 cycle and reminder 4 units of works in next two days. 1 cycle = 3 days ∴ 4 cycle = 12 days And remaining 4 unit work done in next two days. In days 13, A will work 1 unit and in day 14, A and B will work 3 units. Total number the day required to complete the work in the given condition is 14 days

16.

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

17.

A can do a piece of work in 12 days and B in 24 days. If they work together, in how many days will they finish the work ?

(A) 20 days
(B) 8 days
(C) 12 days
(D) 15 days

Solution: Days Eff. Total work A - 12 2 24 B - 12 1 3 A and B together can finish the work $\begin{aligned} = \frac{24}{3} \\ = 8 days \end{aligned}$

18.

There are three boats A, B and C, working together they carry 60 people in each trip. One day an early morning A carried 50 people in few trips alone. When it stopped carrying the passengers B and C started carrying the people together. It took a total of 10 trips to carry 300 people by A, B and C. It is known that each day on an average 300 people cross the river using only one of the 3 boats A, B and C. How many trips it would take to A to carry 150 passengers alone?

(A) 15
(B) 30
(C) 25
(D) 10

19.

B would have taken 10 hours more than what A would have taken to complete a task if each of them worked alone. Working together they can complete the task in 12 hours. How many hours would B take to do 50% of the task?

(A) 30
(B) 15
(C) 20
(D) 10

Solution: Let A completes the work in $x$ hours ∴ B completes the work in $x$ + 10 hours ⇒ A + B complete the work in 12 hours $\begin{aligned} ∴ \frac{x (10 + x)}{10 + x + x} = 12 \\ 10 x + x^{2} = 120 + 24 x \\ x^{2} - 14 x - 120 = 0 \end{aligned}$ On solving, $x$ = 20 hours ∴ B will complete whole work in 20 + 10 = 30 hours Hence, 50% of work will be completed in 15 hours

20.

Two worker A and B are engaged to do a piece of work. A working alone would take 8 hours more to complete the work that when work together. If B worked alone, would take $4 \frac{1}{2}$ hours more than when working together. The time required to finish the work together is = ?

(A) 5 hours
(B) 8 houras
(C) 4 hours
(D) 6 hours

Solution: $\begin{aligned} Let, \\ a = 8h \\ b = 4 \frac{1}{2} h = \frac{9}{2} h \end{aligned}$ Time required to finish the work together $\begin{aligned} = \sqrt{ab} \\ = \sqrt{8 \times \frac{9}{2}} \\ = 6 h \end{aligned}$

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Practice MCQ Questions and Answer on Time and Work

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