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Question Detail
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 it
- 40 days
- 35 days
- 30 days
- 25 days
Answer: Option 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
1. 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 it
- 40 days
- 35 days
- 30 days
- 25 days
Answer: Option 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
2. 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
3. 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.
4. 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 take
- 24 days
- 16 days
- 12 days
- 8 days
Answer: Option 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
5. 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 ?
- 5 days
- 6 days
- 7 days
- 8 days
Answer: Option 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.
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