$12$ men, working $8$ hours a day, complete a piece of work in $10$ days. To complete the same work in $8$ days working $15$ hours a day, the number of men required is

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Solution

The correct option is A $8$
$L e t n u m b e r o f m e n (m_{1}) = 12$
$n u m b e r o f h o u r s (h_{1}) = 8$
$n u m b e r o f d a y s (d_{1}) = 10$
$n u m b e r o f m e n (m_{2}) = x$
$n u m b e r o f h o u r s (h_{2}) = 10$
$n u m b e r o f d a y s (d_{2}) = 8$
$A c c o r d i n g t o g i v e n p r o b l e m$
$m_{2} \times d_{2} \times h_{2} = m_{1} \times d_{1} \times h_{1}$
$\Rightarrow x \times 8 \times 10 = 12 \times 8 \times 10$
$\Rightarrow x = 8$

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