A can do \(1 \over 3\) of a piece of work in 32 days, B can do \(37{1 \over 2}\)% of the same work in 24 days, while C can do 60% of the same work in 48 days. B and C together started and worked for x days. After x days, B left the work and A joined C and both completed the remaining work in (x + 8) days. If the ratio of the work done by (B + C) together to the work done by (A + C) together is 9 ∶ 11, then what fraction of the same work can be completed by C alone in 3.5x days?

Question

Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 25 Jul 2023 Shift 2)

Answer 1

Given:

A can do a piece of work = 96 days

B can do a piece of work = (24 × 200)/75 = 64 days

C can do a piece of work = (48 × 100)/60 = 80 days

Formula used:

Total work = efficiency × time

Calculation:

According to the question:

⇒ (B + C) × x + (A + C) × (x + 8) = 960

⇒ 27 × x + 22 × (x + 8) = 960

⇒ 27x + 22x + 176 = 960

⇒ 49x = 784

⇒ x = 784/49 = 16 days

Total work done by C in 3.5x days = 3.5 × 16 × 12 = 672

Required fraction = 672/960 = 7/10

∴ The correct answer is 7/10.

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