Correct Answer - Option 1 : 240/31 days
Given:
G and J together can complete a piece of work in 8 days.
J and K together can complete same piece of work in 12 days.
G and K together can complete the work in 20 days.
Concepts used:
Total work = LCM
Time = Work/Efficiency
Calculation:
Detailed solution:
LCM of (8, 12 and 20) = 120 = Total work
Efficiency of (G + J) = 120/8 = 15 units/day
Efficiency of (J + K) = 120/12 = 10 units/day
Efficiency of (G + K) = 120/20 = 6 units/day
Total efficiency of 2(G + J + K) = (15 + 10 + 6) units/day = 31 units/day
Efficiency of (G + J + K) = 31/2 units/day
Time taken by A, B and C together = 120 ÷ (31/2) days
⇒ 240/31 days
Short trick:
Time taken by A, B and C to complete a piece of work together = 1/[1/2 × (G 's 1 day work + J's 1 day work + K's 1 day work)]
⇒ 1 ÷ [1/2 × {(1/8) + (1/12) + (1/20)}] days
⇒ 1 ÷ (31/240) days
⇒ 240/31 days
∴ Time taken by A, B and C together is 240/31 days.
