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Question Detail
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.
1. 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
2. 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
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. 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.
5. 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 work.
- 27 days
- 54 days
- 56 days
- 68 days
Answer: Option B
Explanation:
As per question, A do twice the work as done by B.
So A:B = 2:1
Also (A+B) one day work = 1/18
To get days in which B will finish the work, lets calculate work done by B in 1 day =
\begin{aligned}
=\left(\frac{1}{18}*\frac{1}{3} \right) \\
= \frac{1}{54}
\end{aligned}
[Please note we multiplied by 1/3 as per B share and total of ratio is 1/3]
So B will finish the work in 54 days
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