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Question Detail
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 work ?
- 10 hours
- 12 hours
- 16 hours
- 18 hours
Answer: Option 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
1. 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 it ?
- 30 days
- 40 days
- 50 days
- 60 days
Answer: Option 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
2. Rahul and Sham together can complete a task in 35 days, but Rahul alone can complete same work in 60 days. Calculate in how many days Sham can complete this work ?
- 84 days
- 82 days
- 76 days
- 68 days
Answer: Option A
Explanation:
As Rahul and Sham together can finish work in 35 days.
1 days work of Rahul and Sham is 1/35
Rahul can alone complete this work in 60 days,
So, Rahul one day work is 1/60
Clearly, Sham one day work will be = (Rahul and Sham one day work) - (Rahul one day work)
\begin{aligned}
= \frac{1}{35} - \frac{1}{60} \\
= \frac{1}{84} \\
\end{aligned}
Hence Sham will complete the given work in 84 days.
3. 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 days ?
- 3 days
- 4 days
- 5 days
- 6 days
Answer: Option 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
4. 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 day
- 1\5
- 1\6
- 1\7
- 1\8
Answer: Option 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.
5. 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 job.
- \begin{aligned} \frac{4}{9} \end{aligned}
- \begin{aligned} 2\frac{4}{9} \end{aligned}
- \begin{aligned} 3\frac{4}{9} \end{aligned}
- \begin{aligned} 4\frac{4}{9} \end{aligned}
Answer: Option 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}
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