Question

At their usual efficiency levels, A and B together finish a task in 12 days. If A had worked half as efficiently as she usually does, and B had worked thrice as efficiently as he usually does, the task would have been completed in 9 days. How many days would A take to finish the task if she works alone at her usual efficiency?
1. 24
2. 12
3. 18
4. 36

Answer 1

Correct Answer - Option 3 : 18

Calculation:

Men × day = total work

A and B together finish a task in 12 days.

A had worked half as efficiently as she usually does, and B had worked thrice as efficiently as he usually does, the task would have been completed in 9 days.

According to the question,

⇒ (A + B)× 12 = (A/2 + 3B)× 9

⇒ 12A + 12B = (9/2)A + 27B

⇒ (12 – 9/2)A = (27 – 12)B

⇒ 15A = 30B

⇒ A/B = 2/1

A efficiency is 2 unit work in a day, B efficiency is 1 unit work in a day

⇒ total work = (A + B)× 12

⇒ (2 + 1)× 12

⇒ 36 unit

A take to finish the task if she works alone at her usual efficiency

⇒ 36/2

⇒ 18 days

∴ A take to finish the task if she works alone at her usual efficiency would be 18 days.