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A alone can complete a work in 10 days, B alone can complete the same work in 20 days and C alone can complete the same work in 15 days. A and C work together for some time and left, If B worked for 10 days to complete the work, then A and C worked for how many days?

A alone can complete a work in 10 days, B alone can complete the same work in 20 days and C alone can complete the same work in 15 days. A and C work together for some time and left, If B worked for 10 days to complete the work, then A and C worked for how many days? Correct Answer 3 days

Given:

A alone can complete a work in 10 days.

B alone can complete the same work in 20 days.

C alone can complete the same work in 15 days.

Formula:

Total work = Efficiency × Time

Calculation:

Total work = 60 units  (LCM of 10, 20 and 15)

Efficiency of A = 6 units/day

Efficiency of B = 3 units/day

Efficiency of C = 4 units/day

Let A and C worked for x, days

According to the question

(6 + 4) × x + 3 × 10 = 60

⇒ 10x = 60 – 30

⇒ 10x = 30

⇒ x = 30/10

⇒ x = 3 days

∴ A and C work for 3 days.

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