Question

2 men and 7 boys complete a certain piece of work in 8 days. 4 men and 4 boys can do the same in only 6 days. Find the number of days required to complete the work by 1 man.

Answer 1

Let the work done by 1 man in one day be x, and by 1 boy be y,

According to the given conditions,

First condition:

(2x + 7y) × 8 = 1

16x + 56y = 1     ...(1)

Second condition:

(4x + 4y) × 6 = 1

24x + 24y = 1     ...(2)

Now, solving the two equations,

Multiplying equation (1) by 3:

3(16x + 56y) = 3(1)

48x + 168y = 3     ...(3)

Multiplying equation (2) by 7:

7(24x + 24y) = 7(1)

168x + 168y = 7     ...(4)

Subtracting equation (3) from equation (4):

(168x + 168y) − (48x + 168y) = 7 − 3

168x + 168y − 48x − 168y = 4

168x − 48x = 4

120x = 4

x = `4/120`

∴ x = `1/30`

So, 1 man does `1/30` of the work in one day.

Hence, 1 man can complete the work in 30 days.