Question Detail
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 in
- 5 days
- 6 days
- 7.5 days
- 8.5 days
Answer: Option 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}
1. 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 ?
- \begin{aligned} 3\frac{1}{5} min \end{aligned}
- \begin{aligned} 3\frac{2}{5} min \end{aligned}
- \begin{aligned} 3\frac{3}{5} min \end{aligned}
- \begin{aligned} 3\frac{4}{5} min \end{aligned}
Answer: Option 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}
2. 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 in
- \begin{aligned} 13\frac{1}{4} \end{aligned}
- \begin{aligned} 13\frac{1}{2} \end{aligned}
- \begin{aligned} 13\frac{3}{4} \end{aligned}
- \begin{aligned} 13\frac{4}{4} \end{aligned}
Answer: Option 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.
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 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 ?
- 4 days
- 5 days
- 6 days
- 7 days
Answer: Option 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
5. 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.