Question

8men and 12 boys can finish a piece of work in 10 days while 6 men and 8 boys can finish it in 14 days find the time taken by 1 man and a long that by 1 boys alone to finish the work

Answer 1

Let the Work to be Done be : W

Given that 8 Men and 12 Boys can finish the work in 10 days

⇒ 8 Men and 12 Boys can do $[\frac{W}{10}]$ in One Day

⇒ 8M + 12B = $[\frac{W}{10}]$

Multiplying with 6 we get :

⇒ 48M + 72B = $[\frac{6W}{10}]$ ----------------- [1]

Given that 6 Men and 8 Boys can finish the work in 14 days

⇒ 6 Men and 8 Boys can do $[\frac{W}{14}]$ in One Day

⇒ 6M + 8B = $[\frac{W}{14}]$

Multiplying with 8 we get :

⇒ 48M + 64B = $[\frac{8W}{14}]$ ------------------ [2]

Subtracting Equation [2] from Equation [1]

⇒ 48M + 72B - 48M - 64B = $[\frac{6W}{10}]$ - $[\frac{8W}{14}]$

⇒ 8B = $[\frac{3W}{5}]$ - $[\frac{4W}{7}]$

⇒ 8B = $[\frac{21W - 20W}{35}]$

⇒ B = $[\frac{W}{280}]$

⇒ One Boy Does a Work of $[\frac{W}{280}]$ in One Day

⇒ One Boy Can do the Work in 280 Days

Substituting B = $[\frac{W}{280}]$ in 6M + 8B = $[\frac{W}{14}]$

⇒ 6M + $[\frac{8W}{280}]$ = $[\frac{W}{14}]$

⇒ 6M = $\frac{W}{14} - \frac{8W}{280} = \frac{20W - 8W}{280} = \frac{12W}{280} = \frac{3W}{70}$

⇒ M = $[\frac{W}{140}]$

⇒ One Man Can do $[\frac{W}{140}]$ in One Day

⇒ One Man Can do the Work in 140 Days

Answer 2

hope it's clear.............
also 1 boy can do work in 280 days
1 men can do in 140 days