Question

please solve this question shortly​

Answer 1

Let the work to be done be : W

Given : A Man can do the work in 50 days

$\implies \mathsf{Amount\;of\;work\;done\;by\;One\;Man\;in\;one\;day = \dfrac{W}{50}}$

★  Amount of work done by Ten Men in one day :

$\mathsf{\implies \bigg(10 \times \dfrac{W}{50}\bigg) = \bigg(\dfrac{W}{5}}\bigg)}$

Given : Two Boys can do the work in 50 days

$\implies \mathsf{Amount\;of\;work\;done\;by\;Two\;Boy's\;in\;one\;day = \dfrac{W}{50}}$

★  Amount of work done by (8 × 2 = 16) Boys in one day :

$\implies \mathsf{\bigg(8 \times \dfrac{W}{50}\bigg) = \bigg(\dfrac{4W}{25}\bigg)}$

★  Amount of work done by 10 Men & 16 Boys in one day :

$\implies \mathsf{\bigg(\dfrac{W}{5} + \dfrac{4W}{25}\bigg)}$

$\implies \mathsf{\bigg(\dfrac{5W + 4W}{25}\bigg)}$

$\implies \mathsf{\bigg(\dfrac{9W}{25}\bigg)}$

★  Number of days taken by 10 Men & 16 Boys to complete the work :

$\mathsf{\implies \bigg(\dfrac{W \times 1\;day}{\frac{9W}{25}}\bigg)}$

$\mathsf{\implies \dfrac{25}{9}\;days}$