Manoj can do a piece of work in 8 hours. Anand can do it in 8 hours. With the assistance of Anil, they completed the work in 2 hours. In how many hours can Anil alone do it?

Given:

Manoj can do the work in 8 hours

Anand can do the work in 8 hours

All three together do the work in 2 hours

Formula used:

Work rate = 1 ÷ Time

Total work done together = Sum of individual work rates × Time

Calculation:

Manoj's 1 hour work = 1 ÷ 8

Anand's 1 hour work = 1 ÷ 8

Let Anil’s 1 hour work = 1 ÷ x

Together in 1 hour they do:

⇒ (1 ÷ 8) + (1 ÷ 8) + (1 ÷ x) = 1 ÷ 2

⇒ 1 ÷ 4 + 1 ÷ x = 1 ÷ 2

⇒ 1 ÷ x = 1 ÷ 2 − 1 ÷ 4 = (2 − 1) ÷ 4 = 1 ÷ 4

⇒ x = 4

∴ Anil alone can do the work in 4 hours.