Question

The time taken by 4 men to complete the job is double the time taken by 5 children to complete the same job. Each man is twice as fast as women. How long will 12 men, 10 children and 8 women take to complete a job, given that a child would finish the job in 20 days.
(a)2 days
(b)$2\dfrac{1}{8}$ days
(c)4 days
(d)1 day

Answer 1

Hint: We have given how many days it takes for a child to complete the job, with that we will find how much work can 1 child do in 1 day. With that we will find how much work can be done by 1 man and 1 woman in 1 day, with that we will multiply the number of children, man, women.

Complete step-by-step answer:
Since, the time taken by 4 men to complete a job is double the time taken by 5 children to complete the same job.
Since, it is being given that;
1 child would finish the job in 20 days.
So, 5 children will complete it in $\dfrac{20}{5}$ =4 days.
So, work done by 1 child in 1 day would be $\dfrac{1}{20}$ .
Since, it is being given that time by 4 men = 2 times time taken by 5 children.
So, work done by 4 men
 = $2\times 4$ days
 = 8 days.
So, work done by 1 man would be = 32 days.
So, work done by 1 man in 1 day would be $\dfrac{1}{32}$ .
Since, each man is twice as fast as the woman.
So, the same work done by 1 woman would be $32\times 2=64$ days.
So, work done by 1 woman in 1 day would be $\dfrac{1}{64}$ .
Total work by 10 children would be $\dfrac{10}{20}=\dfrac{1}{2}$
Total work by 12 men would be $\dfrac{12}{32}=\dfrac{3}{8}$
Total work by 8 women would be $\dfrac{8}{64}=\dfrac{1}{8}$
Total work by 10 children, 12 men, 8 women would be
$\begin{align}
  & =\dfrac{1}{2}+\dfrac{3}{8}+\dfrac{1}{8} \\
 & =\dfrac{8}{8} \\
 & =1 \\
\end{align}$
Hence option (d) is correct.

Note: The language of the question is a bit tricky, so one should read the question carefully and try to understand the meaning of each information and then try to solve the question. There is always a method to follow to solve this type of questions, which must be learnt, as it helps greatly in exams.