Question

8 men and 12 boy 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 along and that by one boy along to finish the work

Answer 1

total time taken=196 days.

Answer 2

Let the time taken by 1 man alone to finish the work be x days and the time taken by 1 boy alone to finish the work be y days. Then,
1 man's 1 day work = $= \frac{1}{x}$
1 boy's 1 day work = $\frac{1}{y}$
∴8 men's 1 day work =$\frac{8}{x}$
12 boy's 1 day work = $\frac{12}{y}$
∵ 8 men and 12 boy together finish the work in 10 days
$\frac{8}{x}$+$\frac{12}{y}$=$\frac{1}{10}$ ⇒1.
Again, 6 men's 1 day work = $\frac{6}{x}$
8 boy's 1 day work = $\frac{8}{y}$
∵ 6 men and 8 boys can together finish the work in 14 days
$\frac{6}{x}$+$\frac{8}{y}$=$\frac{1}{14}$ ⇒2.
Put $\frac{1}{x}$= X ⇒3. and $\frac{1}{y}$= Y ⇒4.
Then 8X + 12Y= $\frac{1}{10}$ ⇒5.
6X + 8Y = $\frac{1}{14}$ ⇒6.
Multiplying (5) by 3 and (6) by 4
24X + 36Y = $\frac{3}{10}$⇒7.
24X + 32Y = $\frac{2}{7}$⇒8.
Subtracting 8 from 7
4Y = $\frac{1}{70}$
Y= $\frac{1}{280}$
$\frac{1}{y}$= $\frac{1}{280}$
y = 280
Putting Y=$\frac{1}{280}$ in 5.
X=$\frac{1}{140}$
$\frac{1}{x}$ = $\frac{1}{140}$
y= 140
Hence, the time taken by 1 man and 1 boy to finish the work alone are280 days and 140 days respectively.
Hope, it will help you!!