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A, B and C together can complete a work in 25 days. If the ratio of efficiency of A, B and C is 15 ∶ 10 ∶ 6 respectively, then in how many days C alone can complete the same work?
- A727/6
- B725/6
- C775/6
- D745/6
Answer not set
Discussion 1
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CCommunity
Ratio of efficiency of A, B and C = 15 ? 10 ? 6
Ratio of time of A, B and C = 1/15 ? 1/10 ? 1/6 = 2 ? 3 ? 5
Let A alone can complete the work in = 2x days
B alone can complete the work in = 3x days
And C alone can complete the work in = 5x days
According to the question,
1/2x + 1/3x + 1/5x = 1/25
⇒ 31/30x = 1/25
⇒ x = 155/6
So, C alone can complete the work in = 5x = 5 × 155/6 = 775/6 days
Short trick:
Total work = (15 + 10 + 6) × 31 = 31 × 25 = 775
∴ c will complete the work = 775/ 6
Ratio of time of A, B and C = 1/15 ? 1/10 ? 1/6 = 2 ? 3 ? 5
Let A alone can complete the work in = 2x days
B alone can complete the work in = 3x days
And C alone can complete the work in = 5x days
According to the question,
1/2x + 1/3x + 1/5x = 1/25
⇒ 31/30x = 1/25
⇒ x = 155/6
So, C alone can complete the work in = 5x = 5 × 155/6 = 775/6 days
Short trick:
Total work = (15 + 10 + 6) × 31 = 31 × 25 = 775
∴ c will complete the work = 775/ 6