Question

Choose the most appropriate option.
Two men and seven boys can do a work in $14$ days. Three men and eight boys can do the same work in $11$ days. Further eight men and six boys can do three times the amount of this work in:

• A. $18$ days
• B. $30$ days
• C. $24$ days
• D. $21$ days

Answer 1

The correct option is D $21$ days

$2$ men and $7$ boys do one work in $14$ days.

$\therefore$ $2$ men and $7$ boys do a work in $1$ day $=\frac{1}{14}$ work. ----- ( 1 )

$3$ men and $8$ boys do one work in $11$ days.

$\therefore$ $3$ men and $8$ boys do a work in $1$ day $=\frac{1}{11}$ work ----- ( 2 )

Multiply equation ( 1 ) by $3$ we get,

$\therefore$ $6$ men and $21$ boys will do in $1$ day $=\frac{3}{14}$ work ---- ( 3 )

Multiply equation ( 2 ) by $2$ we get,

$\therefore$ $6$ men and $16$ boys will do in $1$ day $=\frac{2}{11}$ work ---- ( 4 )

Now subtracting ( 4 ) from ( 3 ) we get,

$\Rightarrow$ $5$ boys will do work in $1$ day $=\frac{3}{14}-\frac{2}{11}$

$=\frac{5}{154}$work.

$\therefore$ $1$ boy will do work in $1$ day $=\frac{5}{154}\times \frac{1}{5}$

$=\frac{1}{154}$ work.

And $1$ man will do work in $1$ day $=\frac{1}{77}$ work

$\therefore$ The work $8$ men and $6$ boys together will do in $1$ day $=\frac{8}{77}+\frac{6}{154}$

$=\frac{16+6}{154}$

$=\frac{1}{7}$ work.

$\therefore$ $8$ men and $6$ boys together will do $1$ work in $7$ days.

$\therefore$ $8$ men and $6$ boys together will do $3$ times of work in $=3\times 7=21$ days.