Question Detail

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}

1. 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

2. 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 work?

\begin{aligned} 35\frac{1}{2} \end{aligned}
\begin{aligned} 36\frac{1}{2} \end{aligned}
\begin{aligned} 37\frac{1}{2} \end{aligned}
\begin{aligned} 38\frac{1}{2} \end{aligned}

Answer: Option 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

3. 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:

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 in

15 days
10 days
9 days
8 days

Answer: Option 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 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