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 3 days.

∴ (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 xx 3) = 1/18`

⇒ `1/x = 1/18`

⇒ x = 18

On substituting `u = 1/18` in (i), we get:

`2 xx 1/18 + 5v = 1/4`

⇒ `5v = (1/4 - 1/9) = 5/36`

⇒ `v = (5/36 xx 1/5) = 1/36`

⇒ `1/y = 1/36`

⇒ y = 36

Hence, one man alone can finish the work is 18 days and one boy alone can finish the work in 36 days.