Time and Work Questions Answers

Time and Work Questions Answers (MCQ) listings with explanations including questions like determining the time of work, ratio of work done, getting the time by single person when multiple people working on a task etc which are important for many competitive exams.

11) 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 wo

• 1) 6 days
• 2) 7 days
• 3) 8 days
• 4) 9 days
Ans.   B
Explanation :
1 woman's 1 day's work = 1/70 1 Child's 1 day's work = 1/140 5 Women and 10 children 1 day work = \begin{aligned} \left(\frac{5}{70}+\frac{10}{140}\right) \ = \frac{1}{7} \end{aligned} So 5 women and 10 children will finish the work in 7 days.

12) A alone can complete a work in 16 days and B alone can do in 12 days. Starting with A, they work on alternate days. The total work will be completed

• 1) \begin{aligned} 13\frac{1}{4} \end{aligned}
• 2) \begin{aligned} 13\frac{1}{2} \end{aligned}
• 3) \begin{aligned} 13\frac{3}{4} \end{aligned}
• 4) \begin{aligned} 13\frac{4}{4} \end{aligned}
Ans.   C
Explanation :
A's 1 day work = 1/16 B's 1 day work = 1/12 As they are working on alternate day's So their 2 days work = (1/16)+(1/12) = 7/48 [here is a small technique, Total work done will be 1, right, then multiply numerator till denominator, as 7*6 = 42, 7*7 = 49, as 7*7 is more than 48, so we will consider 7*6, means 6 pairs ] Work done in 6 pairs = 6*(7/48) = 7/8 Remaining work = 1-7/8 = 1/8 On 13th day it will A turn, then remaining work = (1/8)-(1/16) = 1/16 On 14th day it is B turn, 1/12 work done by B in 1 day 1/16 work will be done in (12*1/16) = 3/4 day So total days = \begin{aligned} 13\frac{3}{4} \end{aligned} It may be a bit typical question, but if are not getting it in first try then give it a second try. Even not, then comment for explanation for this. We will be happy to help you.

13) 5 men and 2 boys working together can do four times as much work as a man and a boy. Working capacity of man and boy is in the ra

• 1) 1:2
• 2) 1:3
• 3) 2:1
• 4) 2:3
Ans.   C
Explanation :
Let 1 man 1 day work = x 1 boy 1 day work = y then 5x + 2y = 4(x+y) => x = 2y => x/y = 2/1 => x:y = 2:1

14) A can do a certain job in 25 days which B alone can do in 20 days. A started the work and was joined by B after 10 days. The number of days taken in completing the wotk wer

• 1) \begin{aligned} 14\frac{2}{3}kmph \end{aligned}
• 2) \begin{aligned} 15\frac{2}{3}kmph \end{aligned}
• 3) \begin{aligned} 16\frac{2}{3}kmph \end{aligned}
• 4) \begin{aligned} 17\frac{2}{3}kmph \end{aligned}
Ans.   C
Explanation :
Work done by A in l0 days = (1/25) *10 = 2/5 Remaining work = 1 - (2/5) = 3/5 (A+B)s 1 days work = (1/25) + (1/20) = 9/100 9/100 work is done by them in 1 day. hence 3/5 work will be done by them in (3/5)*(100/9) = 20/3days. Total time taken = (10 + 20/3) = 16*(2/3) days

15) Worker A takes 8 hours to do a job. Worker B takes 10 hours to do a job. How long should it take both A and B, working together to do same jo

• 1) \begin{aligned} \frac{4}{9} \end{aligned}
• 2) \begin{aligned} 2\frac{4}{9} \end{aligned}
• 3) \begin{aligned} 3\frac{4}{9} \end{aligned}
• 4) \begin{aligned} 4\frac{4}{9} \end{aligned}
Ans.   D
Explanation :
In this type of questions, first we need to calculate 1 hours work, then their collective work as, A's 1 hour work is 1/8 B's 1 hour work is 1/10 (A+B)'s 1 hour work = 1/8 + 1/10 = 9/40 So both will finish the work in 40/9 hours = \begin{aligned} 4\frac{4}{9} \end{aligned}

16) A and B can together complete a piece of work in 4 days. If A alone can complete the same work in 12 days, in how many days can B alone complete that work

• 1) 4 days
• 2) 5 days
• 3) 6 days
• 4) 7 days
Ans.   C
Explanation :
(A+B)'s 1 day work = 1/4 A's 1 day work = 1/12 B's 1 day work = \begin{aligned} \left( \frac{1}{4} - \frac{1}{12} \right) \= \frac{3-1}{12} \= \frac{1}{6} \\end{aligned} So B alone can complete the work in 6 days

17) A does a work in 10 days and B does the same work in 15 days. In how many days they together will do the same work

• 1) 5 days
• 2) 6 days
• 3) 7 days
• 4) 8 days
Ans.   B
Explanation :
Firstly we will find 1 day work of both A and B, then by adding we can get collective days for them, So, A's 1 day work = 1/10 B's 1 day work = 1/15 (A+B)'s 1 day work = \begin{aligned} \left(\frac{1}{10}+\frac{1}{15} \right) \=\left(\frac{3+2}{30} \right) \= \frac{1}{6} \end{aligned} So together they can complete work in 6 days.

18) A can finish a work in 18 days and B can do same work in half the time taken by A. then working together, what part of same work they can finish in a d

• 1) 1\5
• 2) 1\6
• 3) 1\7
• 4) 1\8
Ans.   B
Explanation :
Please note in this question, we need to answer part of work for a day rather than complete work. It was worth mentioning here because many do mistake at this point in hurry to solve the question So lets solve now, A's 1 day work = 1/18 B's 1 day work = 1/9 [because B take half time than A] (A+B)'s one day work = \begin{aligned} \left(\frac{1}{18}+\frac{1}{9} \right) \\ =\left(\frac{1+2}{18} \right) \\ = \frac{1}{6} \end{aligned} So in one day 1/6 work will be done.

19) A tyre has two punctures. The first puncture alone would have made the tyre flat in 9 minutes and the second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat

• 1) \begin{aligned} 3\frac{1}{5} min \end{aligned}
• 2) \begin{aligned} 3\frac{2}{5} min \end{aligned}
• 3) \begin{aligned} 3\frac{3}{5} min \end{aligned}
• 4) \begin{aligned} 3\frac{4}{5} min \end{aligned}
Ans.   C
Explanation :
Do not be confused, Take this question same as that of work done question's. Like work done by 1st puncture in 1 minute and by second in 1 minute. Lets Solve it: 1 minute work done by both the punctures = \begin{aligned} \left(\frac{1}{9}+\frac{1}{6} \right) \\ =\left(\frac{5}{18} \right) \\ \end{aligned} So both punctures will make the type flat in \begin{aligned} \left(\frac{18}{5} \right)mins \\ = 3\frac{3}{5} mins \end{aligned}

20) A is twice as good as workman as B and together they finish a piece of work in 18 days. In how many days will B alone finish the wor

• 1) 27 days
• 2) 54 days
• 3) 56 days
• 4) 68 days