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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.

1) A can do a job in 16 days, B can do same job in 12 days. With the help of C they did the job in 4 days. C alone can do the same job in how many days

  • 1) \begin{aligned} 6\frac{1}{2}days \end{aligned}
  • 2) \begin{aligned} 7\frac{1}{2}days \end{aligned}
  • 3) \begin{aligned} 8\frac{3}{5}days \end{aligned}
  • 4) \begin{aligned} 9\frac{3}{5}days \end{aligned}
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Ans.   D
Explanation :
In this question we having, A's work, B's work and A+B+C work. We need to calculate C's work. We can do it by, (A+B+C)'s work - (A's work + B's work). Let's solve it now: C's 1 day work = \begin{aligned} \frac{1}{4}- \left(\frac{1}{16} +\frac{1}{12} \right) \\ =\left(\frac{1}{4} - \frac{7}{48} \right) \\ = \frac{5}{48} \end{aligned} So C can alone finish the job in 48/5 days, Which is = \begin{aligned} 9\frac{3}{5}days \end{aligned}

2) To complete a work A and B takes 8 days, B and C takes 12 days, A,B and C takes 6 days. How much time A and C will ta

  • 1) 24 days
  • 2) 16 days
  • 3) 12 days
  • 4) 8 days
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Ans.   D
Explanation :
A+B 1 day work = 1/8 B+C 1 day work = 1/12 A+B+C 1 day work = 1/6 We can get A work by (A+B+C)-(B+C) And C by (A+B+C)-(A+B) So A 1 day work = \begin{aligned} \frac{1}{6}- \frac{1}{12} \\ = \frac{1}{12} \end{aligned} Similarly C 1 day work = \begin{aligned} \frac{1}{6}- \frac{1}{8} \\ = \frac{4-3}{24} \= \frac{1}{24} \end{aligned} So A and C 1 day work = \begin{aligned} \frac{1}{12} + \frac{1}{24} \\ = \frac{3}{24} \= \frac{1}{8} \end{aligned} So A and C can together do this work in 8 days

3) A does half as much work as B in three-fourth of the time. If together they take 18 days to complete the work, how much time shall B take to do

  • 1) 40 days
  • 2) 35 days
  • 3) 30 days
  • 4) 25 days
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Ans.   C
Explanation :
Suppose B takes x dáys to do the work. As per question A will take \begin{aligned} 2* \frac{3}{4} * x = \frac{3x}{2}days \end{aligned} (A+B)s 1 days work= 1/18 1/x + 2/3x = 1/18 or x = 30 days

4) A is thrice as good a workman as B and takes 10 days less to do a piece of work than B takes. B alone can do the whole work

  • 1) 15 days
  • 2) 10 days
  • 3) 9 days
  • 4) 8 days
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Ans.   A
Explanation :
Ratio of times taken by A and B = 1:3 Means B will take 3 times which A will do in 1 time If difference of time is 2 days, B takes 3 days If difference of time is 10 days, B takes (3/2) * 10 =15 days

5) A can do a piece of work in 15 days and B alone can do it in 10 days. B works at it for 5 days and then leaves. A alone can finish the remaining work

  • 1) 5 days
  • 2) 6 days
  • 3) 7.5 days
  • 4) 8.5 days
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Ans.   C
Explanation :
B's 5 days work = \begin{aligned} \frac{1}{10}*5 = \frac{1}{2} \ \text{Remaining work =} 1-\frac{1}{2} \ = \frac{1}{2} \ \text{A can finish work =}15*\frac{1}{2} \= 7.5 days \end{aligned}

6) A completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining work in 3 days. How long does it need for B if he alone completes the wo

  • 1) \begin{aligned} 35\frac{1}{2} \end{aligned}
  • 2) \begin{aligned} 36\frac{1}{2} \end{aligned}
  • 3) \begin{aligned} 37\frac{1}{2} \end{aligned}
  • 4) \begin{aligned} 38\frac{1}{2} \end{aligned}
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Ans.   C
Explanation :
Work done by A in 20 days = 80/100 = 8/10 = 4/5 Work done by A in 1 day = (4/5) / 20 = 4/100 = 1/25 --- (1) Work done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B) Work done by A and B in 1 day = 1/15 ---(2) Work done by B in 1 day = 1/15 – 1/25 = 2/75 => B can complete the work in 75/2 days = 37 (1/2) days

7) A can do a piece of work in 4 hours . A and C together can do it in just 2 hours, while B and C together need 3 hours to finish the same work. In how many hours B can complete the wor

  • 1) 10 hours
  • 2) 12 hours
  • 3) 16 hours
  • 4) 18 hours
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Ans.   B
Explanation :
Work done by A in 1 hour = 1/4 Work done by B and C in 1 hour = 1/3 Work done by A and C in 1 hour = 1/2 Work done by A,B and C in 1 hour = (1/4)+(1/3) = 7/12 Work done by B in 1 hour = (7/12)–(1/2) = 1/12 => B alone can complete the work in 12 hour

8) 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 t

  • 1) Rs. 300
  • 2) Rs. 400
  • 3) Rs. 500
  • 4) Rs. 600
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Ans.   B
Explanation :
C's 1 day's work = \begin{aligned} \frac{1}{3}- \left(\frac{1}{6} +\frac{1}{8} \right) \\ =\left(\frac{1}{3} - \frac{7}{24} \right) \\ = \frac{1}{24} \A:B:C = \frac{1}{6}:\frac{1}{8}:\frac{1}{24} \= 4:3:1 \C's Share = \frac{1}{8}* 3200 \ = 400 \end{aligned} If you are confused how we multiplied 1/8, then please study ratio and proportion chapter, for small information, it is the C ratio divided by total ratio.

9) 4 men and 6 women finish a job in 8 days, while 3 men and 7 women finish it in 10 days. In how many days will 10 women working together finish i

  • 1) 30 days
  • 2) 40 days
  • 3) 50 days
  • 4) 60 days
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Ans.   B
Explanation :
Let 1 man's 1 day work = x and 1 woman's 1 days work = y. Then, 4x + 6y = 1/8 and 3x+7y = 1/10 solving, we get y = 1/400 [means work done by a woman in 1 day] 10 women 1 day work = 10/400 = 1/40 10 women will finish the work in 40 days

10) A piece of work can be done by 6 men and 5 women in 6 days or 3 men and 4 women in 10 days. It can be done by 9 men and 15 women in how many day

  • 1) 3 days
  • 2) 4 days
  • 3) 5 days
  • 4) 6 days
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Ans.   A
Explanation :
To calculate the answer we need to get 1 man per day work and 1 woman per day work. Let 1 man 1 day work =x and 1 woman 1 days work = y. => 6x+5y = 1/6 and 3x+4y = 1/10 On solving, we get x = 1/54 and y = 1/90 (9 men + 15 women)'s 1 days work = (9/54) + (15/90) = 1/3 9 men and 15 women will finish the work in 3 days
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