Prem can do a piece of work in 112 days. Ben can do this work in 90 days. Prem started the work alone. After how many days should Ben join him, so that the total work is finished in 56 days?

Question

Question

This question was previously asked in

SSC GD Constable (2022) Official Paper (Held On : 08 Feb 2023 Shift 3)

Answer 1

Given

Prem's work time = 112 days

Ben's work time = 90 days

Total time to finish the work = 56 days

Concept:

In the scenario of combined work, (Total work) = (Work rate) × (Time), where work rate is the inverse of the time taken to finish the work alone.

Calculation:

⇒ Prem's work rate = 1/112 per day

⇒ Ben's work rate = 1/90 per day

⇒ Combined work rate = Prem's work rate + Ben's work rate = 1/112 + 1/90 = 1/56 per day

The total number of days Ben works be x

So, Prem works for 56 days and Ben works for x days to complete work

56/112 + x/90 = 1

⇒ 56 × 45 + 56x = 112 × 45

⇒ 56x + 6272 - 112x = 112 × 45 - 56 × 45

⇒ 56x = 56 × 45

⇒ x = 45

Ben join after 56 - 45 = 11 days

Hence, Ben should join Prem after 11 days.

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