Correct Answer - Option 3 : 6
Given,
Number of days taken by 2 Men and 7 women to complete the work in = 7 days
Number of days taken by 7 women to complete the work = 8 days
Concept used,
If someone completes work in X days
∴ Work done in 1 day = 1/X
Calculation
Let 1 day’s work of a man work is X and 1 day’s work of a woman is Y.
∵ 7 women can complete that work in 8 days
∴ Work done by 7 women in 8 days = 1
⇒ 7 × 8Y = 1
⇒ 56Y = 1
⇒ Y = 1/56
∵ 2 Men and 7 women can do a piece of work in 7 days
∴ Work done by 2 men and 7 women in 7 days = 1
⇒ 7 × (2X + 7Y) = 1
⇒ 2X + 7Y = 1/7
⇒ 2X + (7 × 1/56) = 1/7
⇒ 2X + 1/8 =1/7
⇒ 2X = 1/7 – 1/8
⇒ 2X = 1/56
⇒ X = 1/112
Let Z men are needed with 4 women to complete a work in 8 days
∴ Work done by Z men and 4 women in 8 days = 1
⇒ Z/112 + 4/56 = 1/8
⇒ Z/112 + 1/14 = 1/8
⇒ Z/112 = 1/8 – 1/14
⇒ Z/112 = 3/56
⇒ Z = 6
∴ 6 men are needed with 4 women to complete a work in 8 days.
