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A, B and C can complete a work in x, 30 and 45 days, respectively. B and C worked together for 6 days. The remaining work was completed by A alone in 12 days. The value of x is:
1. 24
2. 20
3. 18
4. 15

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Correct Answer - Option 3 : 18

Given:

Time taken to complete the work by A = x days

Time taken to complete the work by B = 30 days

Time taken to complete the work by C = 45 days

Time taken to complete the work by B and C together = 6 days

Remaining work completed by A = 12 days

Formula used:

Work = Efficiency × Time

Calculation:

LCM of 30 and 45 is 90

Efficiency of B = 90/30 = 3 units/day

Efficiency of C = 90/45 = 2 units/day

Total units of work by B and C together = [(3 + 2) × 6]

⇒ 30 units

Efficiency of B and C together = (90 – 30) = 60 units

Efficiency of A = (60/12) = 5 units/day

Remaining work completed by A = (90/5) days

⇒ x = 18 days

∴ The value of x is 18

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