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In the following question, two statements are numbered as I and II. On solving these statements, we get quantities I and II respectively. Solve both quantities and choose the correct option. Quantity I: 3 men or 4 women can complete a piece of work in 5 days. In how many days can 2 men and 3 women complete same piece of work? Quantity II: 11 days

In the following question, two statements are numbered as I and II. On solving these statements, we get quantities I and II respectively. Solve both quantities and choose the correct option. Quantity I: 3 men or 4 women can complete a piece of work in 5 days. In how many days can 2 men and 3 women complete same piece of work? Quantity II: 11 days Correct Answer Quantity 1 < Quantity 2

Quantity I:

1 day work done by individual = Work/time

⇒ 1 day work of 1 man = 1/(3 × 5) = 1/15

⇒ 1 day work of 2 men = 2/15 

1 day work of 1 woman = 1/(4 × 5) = 1/20

⇒ 1 day work of 3 women = 3/20

⇒ 1 day work of 2 men and 3 women = (2/15) + (3/20) = 17/60

⇒ Time = Work/Efficiency

Time taken by 2 men and 3 women to complete work together = 1/(17/60) days = 60/17 days

∴ 2 men and 3 women can complete a piece of work in 60/17 days. 

Quantity II: 11 days

∴ Quantity I < Quantity II

 

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