Question

A man can do a piece of work in $5$ days. He and his son working together can finish it in $3$ days. In how many days can the son do it alone?

• A. $6^{1/2}$ days
• B. $7$ days
• C. $7^{1/2}$ days
• D. $8$ days

Answer 1

The correct option is C $7^{1/2}$ days

We know that ,
Number of days man required to do piece of work $=5$ days
Number of days his son required to do piece of work $=3$ days

Let us consider number of days both man and his son require $=x$ days

$\therefore$ We can calculate work done by man in $1$ hour $=1/5$
Work done by his son in $1$ hour $=1/x$
Now, work done by both man and his son together in a $1$ hour $=1/3$

Also the work done by both man and his son together in $1$ hour is equal to the sum of the work done by each of them in $1$ hour $=1/5+1/x=(x+5)/5x$

Therefore,

$(x+5)/5x=1/3$
$3x+15=5x$
$2x=15$
$x=15/2$

$x=7^{1/2}$

$\therefore$ Son alone can do work together in $7^{1/2}$ days