A, B and C can finish a work in 10, 15 and 30 days, respectively. In how many days can A finish the work if he is assisted by B and C both every third day?

Question

Question

This question was previously asked in

SSC GD Constable (2022) Official Paper (Held On : 13 Feb 2023 Shift 1)

Answer 1

Given:

A can finish a work in 10 days

B can finish a work in 15 days

C can finish a work in 30 days

Concept:

Total work is calculated by the LCM of the time taken by each, and total work done in a day is the sum of each's work done in a day.

Solution:

⇒ Total work = LCM of 10, 15, 30 = 30 units

⇒ Work done by A in a day = 30/10 = 3 units

⇒ Work done by B in a day = 30/15 = 2 units

⇒ Work done by C in a day = 30/30 = 1 unit

⇒ Total work done in 3 days = 3 + 3 + (3 + 2 + 1) = 12 units

⇒ Total work done in 6 days = 12 + 12 = 24 units

So Remaining work = 30 - 24 = 6 units

On 7th and 8th day, A works and complete the work = 3 + 3 = 6 units

Work completed in 8 days = 24 + 6 = 30 units = Total work

Hence, A can finish the work in 8 days when assisted by B and C every third day.