19 men and 22 women working 6 hours per day can do 4/7 of a work in 21 days and the remaining part of the work is done by 25 men and 38 women working 9 hour per day in 7 day. Find the number of days for 14 men and 10 women to complete the entire work by working 7 hour per day

Given:

19 men and 22 women work 6 hours/day for 21 days and complete 4/7 of the work.

25 men and 38 women work 9 hours/day for 7 days and complete the remaining 3/7 of the work.

Formula used:

M₁ × D₁ × H₁ / W₁ = M₂ × D₂ × H₂ / W₂ = Total work

Where M = number of men, D = number of days, H = number of hours per day, W = amount of work.

Calculation:

Let 'm' be the work done by one man in one hour and 'w' be the work done by one woman in one hour.

According to the question,

(19m + 22w) × 21 × 6 / (4/7) = (25m + 38w) × 7 × 9 / (3/7) 

⇒ (19m + 22w) × 9 = (25m + 38w) × 6

⇒ 171m + 198w = 150m + 228w

⇒ 21m = 30w

⇒m/w = 10/7

Now, let the total work is completed in D days by 14 men and 10 women working 7 hour per day.

Then

(14m + 10w) × D × 7  = (25m + 38w) × 7 × 9 / (3/7) = Total work

⇒ (14 × 10 + 10 × 7) × D × 7  = (25 × 10 + 38 × 7) × 7 × 9 / (3/7) 

⇒ 210 × D = 516 × 21

⇒ D = 51.6 days.