Question

If $6$ men and $8$ boys can do a piece of work in $10$ days and $26$ men and $48$ boys can do same in $2$ days, the time taken by $15$ men and $20$ boys to do the same type of work will be :

• A. $5$ days
• B. $4$ days
• C. $6$ days
• D. $7$ days

Answer 1

The correct option is B $4$ days

Let $1$ man's $1$ day's work $=x$ and $1$ boy's $1$ day's work $=y$.
Then, $6x+8y=\frac{1}{10}$ and $26x+\frac{481}{2}$

Solving these two equation, we get :
$x=\frac{1}{100}$ and $y=\frac{1}{200}$
($15$ men $+20$ boy)'s $1$ day's work $=(\frac{15}{100}+\frac{20}{200})=\frac{1}{4}$
So, $15$ men and $20$ boys can do the work in $4$ days.