Rakshit, Ajay, and Satish are sanitation workers in a Municipal Corporation. Rakshit alone takes 20 hours to clean a drain while Ajay takes 12 hours when working alone to do the same. All three together take only 5 hours to clean the drain. In how many hours, can Satish complete the work alone?

Question

Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 17 Jul 2023 Shift 1)

Answer 1

GIVEN:

Rakshit, Ajay, and Satish together take only 5 hours to clean the drain

Rakshit alone can finish the work in 20 days.

Ajay alone can finish the work in 12 days.

FORMULA USED:

Time = Work / Efficiency

CALCULATION:

⇒ 1-day work of Rakshit, Ajay, and Satish = 1 / 5 units

Rakshit alone can finish the work in 20 days

⇒ 1 day work of Salman = 1 / 20 units

Ajay alone can finish the work in 12 days

⇒ 1 day work of Salman = 1 / 12 units

Suppose the number of days taken by Satish alone to finish the work is x

⇒ 1 day work of Satish = 1 / x units

Accordingly,

">⇒ 1 / 5 = 1 / 20 + 1 / 12 + 1 / x

">⇒ 1 / x = 1 / 5 - 1 / 20 + 1 / 12

⇒ 1 / x = (12 - 8) / 60

⇒ x = 15 days.

The number of days taken by Satish alone to finish the work is 15 days.

Alternate Method ">Alternate Method Suppose total work is 60 units (LCM of 5, 12 and 20)

Efficiency of all three = 60 / 5 = 12

Efficiency of Rakshit = 60 / 20 = 3

Efficiency of Ajay = 60 / 12 = 5

Efficiency of Satish = (12 - 8) = 4

∴ Number of days taken by Satish alone to finish the work = 60 / 4 = 15 days