Answer:
Option A
Explanation:
I. $(10\times 6)$ men can complete the work in $1$ day.
$\Rightarrow$ $1$ boy's $1$ day's work $=\frac{1}{60}$.
II. $\left(10\times\frac{24}{7}\right)$ boys+ $\left(10\times\frac{24}{7}\right)$ girls can complete the work in $1$ day.
$\Rightarrow\left(\frac{240}{7}\right)$ boy's $1$ day work + $\left(\frac{240}{7}\right)$ girl's $1$ day work $=1$.
$\Rightarrow$ $\left(\frac{240}{7}\times\frac{1}{60}\right)$ + $\left(\frac{240}{7}\right)$ girl's $1$ day's work $=1$.
$\Rightarrow$ $\left(\frac{240}{7}\right)$ girl's $1$ day's work $=\left(1-\frac{4}{7}\right)$ $=\frac{3}{7}$.
$\Rightarrow$ $10$ girl's $1$ day work $=\left(\frac{3}{7}\times\frac{7}{240}\times 10\right)$ $=\frac{1}{8}$.
So, $10$ girls can finish the work in $8$ days.
III. ($10$ boy's work for $3$ days) + ($10$ girl's work for $4$ days) $=1$.
$\Rightarrow$ $(10\times 3)$ boy's $1$ day work + $(10\times 4)$ girl's $1$ day's work $=1$.
$\Rightarrow$ $30$ boy's $1$ day work + $40$ girl's $1$ day's work $=1$.
Thus, I and II will give us the answer.
And, II and III will give us the answer.
$\therefore$ Correct answer is (A).
