Given:

The efficiency of A = 5 × the efficiency of B

Then ratio of efficiency of A to the efficiency of B = 5 : 1

A can complete a work in 60 days less than B.

Concept used:

Days is inversely proportional to efficiency

If A does a work in x days and B does a work in y days, the ratio of days = x : y and

The ratio of efficiency = y : x

If a person does a work in ‘n’ days then one day work by a person will be 1/n part of total work

Calculation:

Let the efficiency of A and B be 5x and x respectively.

Then the number of days taken by A and B for a work will be x and 5x respectively

A takes less time than B = 5x – x

⇒ A – B = 4x days

According to question, A – B = 60 days

⇒ 4x = 60

⇒ x = 60/4

⇒ x = 15

Then A takes days to complete a work = x

⇒ 15 days

Now one day work by A = 1/15

B takes days to complete a work = 5x

⇒ 5 × 15

⇒ 75 days

Now one day work by B = 1/75

One day work when both work together = one day work by A + one day work by B

⇒ 1/15 + 1/75

⇒ (5 + 1)/75

⇒ 6/75

⇒ 2/25

⇒ 1/12.5

Now, one work completed by both A and B = 12.5 days

∴ The work would be completed by both in 12.5 days