Question

3 men and 2 women can complete a work in 18 days and 4 men and 5 women can complete the same work in 12 days. How many women can complete the same work in 14 days?
1. 24
2. 30
3. 12
4. 18

Answer 1

Correct Answer - Option 4 : 18

Given:

Total time taken by (3 Men + 2 Women) = 18 days

Total time taken by (4 Men + 5 Women) = 12 days

 

Concept:

Determine the efficiency of Men with respect to woman.

Formula used:

M₁D₁ = M₂D₂

Calculation:

∵ (3 Men + 2 Women) × 18 = (4 Men + 5 Women) × 12

⇒ (3 Men + 2 Women) × 3 = (4 Men + 5 Women) × 2

⇒ 9 Men + 6 Women = 8 Men + 10 Women

⇒ 1 Man = 4 Women      ------(1)

Let the number of women be ‘y’

∴ (3 Men + 2 Women) × 18 = y × 14

⇒ (12 Women + 2 Women) × 18 = 14y      ------(From 1)

⇒ 14 Women × 18 = 14y

⇒ y = 18 days