P, Q and R can complete a work alone in 12,15 and 20 days respectively. They started the work together. P left the work 8 days before the work was completed and Q left the work 5 days after P had left. R completed the remaining work alone. How many days will be required to complete the whole work?

Question

Question

This question was previously asked in

SSC CHSL Tier-I Exam 2022 Official Paper (Held On: 15 March, 2023 Shift 4)

Answer 1

Given:

P can complete the work in 12 days.

Q can complete the work in 15 days.

R can complete the work in 20 days.

P left the work 8 days before it was completed.

Q left the work 5 days after P had left.

R completed the remaining work alone.

Concept:

The total work done by individuals working together is equal to the sum of their individual work done in the same time.

Solution:

Total work = LCM(12, 15, 20) = 60

Efficiency of P = 60/12 = 5

Efficiency of Q = 60/15 = 4

Efficiency of R = 60/20 = 3

Let the total work done in t days.

According to question,

⇒ 5(t - 8) + 4(t - 3) + 3t = 60

⇒ 5t - 40 + 4t - 12 + 3t = 60

⇒ 12t = 112

⇒ t = 112/12 = 28/3 days

∴ 28/3 days will be required to complete the whole work.