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