Question

A and B can do a work together in 18 days. A is three times as efficient as B. In how many days can B alone complete the work?

• A. 54 days
• B. 64 days
• C. 72 days
• D. 60 days

Answer 1

Answer:

C. 72 days

Solution:

Given:

A and B can do the work together in 18 days. A is three times as efficient as B.

Concept Used:

Time ∝ 1/efficiency

If a person can complete a work in x days then in 1 day he will do 1/x part of the work

Calculation:

A is three times as efficient as B which imply the rate of efficiency of A and B is 3 : 1

Required time ratio of A and B to complete the work alone is 1/3 : 1

⇒ 1 : 3

Let, A can do the work in x day and B can do the same in 3x day

In 1 day A can do 1/x part of the work

In 1 day B can do 1/3x part of the work

Together in 1 day they can do (1/x + 1/3x) part of the work

⇒ 4/3x part of the work

A and B can do the work together in 18 days.

In 1 day they can do 1/18 part of the work together

4/3x = 1/18

⇒ x = 24

B alone take time to complete the work (3 × 24)

⇒ 72 days

∴ In 72 days B can complete the work alone.

Alternate Method: