Question

8 men and 12 boys can finish a piece of work in 5 days, while 6 men and 8 boys can finish it in 7 days. Find time taken by a man and a boy alone to finish the same work.

• A. 80, 150
• B. 50, 120
• C. 60, 130
• D. 70, 140

Answer 1

The correct option is D 70, 140

Let 1 man can finish the work in x days and let 1 boy can finish the work in y days.

1 man’s one day work = $\frac{1}{x}$
1 boy’s one day work = $\frac{1}{y}$
According to the question,
8 men’s 1 day’s work + 12 boy’s one day’s work = $\frac{1}{5}$
⇒ $\frac{8}{x}$ + $\frac{12}{y}$ = $\frac{1}{5}$
⇒ 8u + 12v = $\frac{1}{5}$ ….(i)
where u = $\frac{1}{x}$ and v = $\frac{1}{y}$
Similarly, 6u + 8v = $\frac{1}{7}$ ….(ii)
On solving (i) and (ii) we get, x = 70 and y = 140
∴ One man alone can finish the work in 70 days and one boy alone can finish the work in 140 days.

Answer - 70, 140