Question

2 men and 5 boys can finish a piece of work in 4 days, while 3 men and 6 boys can finish it in 3 days. Find the time taken by one man alone to finish the work and that taken by one boy alone to finish the work.

Answer 1

Let us suppose that one man alone can finish the work in x days and one boy alone can finish it in y days.
∴ One man’s one day’s work = `1/x`
And, one boy’s one day’s work = `1/y`
2 men and 5 boys can finish the work in 4 days.
∴ (2 men’s one day’s work) + (5 boys’ one day’s work) =` 1/4`
`⇒ 2/x + 5/y = 1/4`
⇒ 2u + 5v = `1/4`          …….(i)    Here, `1/x= u and 1/y`= v
Again, 3 men and 6 boys can finish the work in 3days.
∴ (3 men’s one day’s work) + (6 boys’ one day’s work) = `1/3`
`⇒ 3/x + 6/y = 1/3`
⇒ 3u + 6v = `1/3` …….(ii)    Here, `1/x = u and 1/y = v`
On multiplying (iii) from (iv), we get:
`3u = (5/3− 6/4) = 2/12 = 1/6`
`⇒ u = 1/(6 × 3) = 1/18 ⇒ 1/x = 1/18 ⇒ x = 18`
On substituting u = `1/1`8 in (i), we get:
`2 × 1/18 + 5v = 1/4 ⇒ 5v = (1/4− 1/9) = 5/36`
`⇒ v = (5/36 × 1/5) = 1/36 ⇒ 1/y = 1/36 ⇒ y = 36`
Hence, one man alone can finish the work is 18days and one boy alone can finish the work in 36 days.