Question

If $34$ men completed $\frac{2}{5}$th of a work in $8$ days working $9$ hours a day. How many more man should be engaged to finish the rest of the work in $6$ days working $9$ hours a day?

• A. $68$ men
• B. $45$ men
• C. $34$ men
• D. $28$ men
• E. None of these

Answer 1

The correct option is C $34$ men

Work efficiency of $34$ men in $8$ days working $9$ hours a day is $\frac{2}{5}$th

Hence, work efficiency of $x$ men to finish rest of the work in $6$ days working $9$ hours a day = $1-\frac{2}{5}=\frac{3}{5}$

$\therefore$ By direct proportionality,

$\frac{34\times 8\times 9}{\frac{2}{5}}=\frac{x\times 6\times 9}{\frac{3}{5}}$

$\therefore 34\times 72\times \frac{3}{5}=x\times 54\times \frac{2}{5}$

$\therefore x=\frac{34\times 72\times 3\times 5}{54\times 2\times 5}$

$\therefore x=68$

Hence extra men required = $68-34=34$men

So, the answer is option C