P1 and P2 can do a piece of work together in 14 days, P2 and P3 can do the same work together in 21 days, while P3 and P1 can do it together in 42 days. How much work can all the 3 together do in 12 days?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 6/7.
Explanation :
P1 + P2 = 14 days
P2 + P3 = 21 days
P3 + P1 = 42 days
Let the total work done by P1, P2, P3 be LCM of (14, 21, 42) = 42 units
Efficiency of (P1 + P2) = 42/14 = 3 units/day
Efficiency of (P2 + P3) = 42/21 = 2 units/day
Efficiency of (P3 + P1) = 42/42 = 1 unit/day
(P1 + P2 + P3) = 6/2 = 3 units/day
Therefore work done by (P1 + P2 + P3) in 12 days = 12 × 3 = 36 units
The fraction of work done by (P1 + P2 + P3) in 12 days of the total work = 36/42 = 6/7