Correct Answer - Option 2 : 55/2 days
Given
3 men and 4 female can do work in = 15 days
5 men and 3 female can do work in = 10 days
Formula Used:
Work = Time × Efficiency
Calculation:
⇒ let the efficiency of men and female be M and W
⇒ 3M + 4W = 15 , 5M + 3W = 10
⇒ LCM (15,10) = 30
⇒ Let total work = 30
⇒ efficiency of 3M + 4W = 2 ----(1)
⇒ similarly, 5M + 3W = 3 -----(2)
multiply the equation (1) by 3 and equation (2) by 4
⇒ 9M + 12W = 6 ------(1)
⇒ 20M + 12W = 12 -----(2)
⇒ From (3) and (4)
⇒ M = 6/11
⇒ total efficiency of 2 men = 12/11
⇒ No. of days taken by 2 men to complete the work = 30 × 11/12 = 55/2 days
⇒ No. of days taken by 2 men to complete the work is 55/2 days