Question

2 men and 3 women working 7 hours a day finish a work in 5 days 4 men and 4 women working 3 hours a day do the same work in 7 days find the number of days in which the work is done by 7 men only working 4 hours a day

Answer 1

Case 1 :- 2 men and 3 women working 7 hours a day finish a work in 5days .
Case 2 :- 4 men and 4 women working 3 hours a day finish same work in 7 days .

use formula,
M₁D₁H₁ = M₂D₂H₂
Here, M denotes number of people
D denotes number of days
H denotes hours

Given, M₁ = (2m + 3w), D₁ = 5 days and H₁ = 7 hrs
M₂ = (4m + 4w) , D₂ = 7 days and H₂ = 3 hrs

Now, (2m + 3w) × 5 × 7 = (4m + 4w) × 7 × 3
⇒70m + 105w = 84m + 84w
⇒21w = 14m
⇒3w = 2m

Now, apply , M₃D₃H₃ = M₁D₁H₁
M₃ = 7m , D₃ = ? And H₃ = 4 hrs
M₁ = (2m + 3w) =( 2m + 2m) = 4 m [ ∵ 3w = 2m ]
D₁ = 5 days and H₁ = 7 hours

Now, 7 × D₃ × 4 = 4 × 5 × 7
D₃ = 5 days