Question

Given, 8 men can dig a pit in 20 days. If a man works one and a half as much again as a boy, then 4 men and 8 boys can dig it in
A. 10 days
B. 12 days
C. 15 days
D. 17 days

Answer 1

Hint: First we will calculate the total work then we will calculate the total work done by 4 men and 8 boys together. Then by dividing the total work by work done by 4 men and 8 boys together we will get the number of days.

Complete step by step solution:
We have been given that 8 men can dig a pit in 20 days and a man works one and a half as much again as a boy.
We have to find out how many days 4 men and 8 boys can dig it.
Now, we have given that a man works one and a half as much again as a boy.
So if the work done by a boy will be $=1$
Then the work done by a man will be $=1+\dfrac{1}{2}$
So we will get the ratio of work done by a man and boy as $3:2$
Now, the total work will be
$\begin{align}
  & \Rightarrow 8\times 3\times 20 \\
 & \Rightarrow 480 \\
\end{align}$
Now, the total work done by 4 men and 8 boys will be
$\begin{align}
  & \Rightarrow 4\times 3+8\times 2 \\
 & \Rightarrow 12+16 \\
 & \Rightarrow 28 \\
\end{align}$
Now, time taken to dig a pit by 4 men and 8 boys will be
$\begin{align}
  & \Rightarrow \dfrac{480}{28} \\
 & \Rightarrow 17.14 \\
\end{align}$
So the number of days 4 men and 8 boys take to dig a pit are 17 days.

Note:
Here in this particular question we get the answer as decimal. But we have to find the number of days so we convert the decimal number into the whole number by approximating the value to the nearest number. We cannot take a number of days into decimal.