Given Data:
3 men and 2 women can finish a job in 120/13 days
2 men and 3 women can finish the same job in 10 days
Concept:
We need to solve these equations to find the time one man and one woman can finish the job.
Solution:
Work done in both case is equal, so
⇒ (3M + 2W) × 120/13 = (2M + 3W) × 10
Solving these equations, we get:
⇒ M : W = 3 : 2
Total work = (3 × 3 + 2 × 2) × 120/13 = 120 units
One man and one woman start working and after 12 days, one more man joins the work. So:
⇒ (3 + 2) × 12 = 60 units
Remaining work = 120 - 60 = 60 units
1 more man joins the work. So after three more days work completed = (2 × 3 + 2) × 3 = 24 units
Remaining work = 60 - 24 = 36 units
To engage more men or women to finish the work the next day,
(2 + X) × 3 + (1 + Y) × 2 = 36
⇒ 6 + 3X + 2 + 2Y = 36
⇒ 3X + 2Y = 28
If all men are joining then put Y = 0
⇒ 3X = 28
⇒ X = 9.33 or approx 10 men
If all women are joining then put X = 0
⇒ 2Y = 28
⇒ Y = 14 women
Therefore, to finish the work as per direction, a minimum of either 14 women or 10 men must be engaged.