A and B can do a piece of work in 14/3 days while B and C can do the same work in 12/5 days and C and A in 16/3 days. By working together what part of the same work all three can finish in 2 days?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 275/336.
A and B can do a piece of work in 14/3 days while B and C can do the same work in 12/5 days and C and A in 16/3 days
Rate of A and B = 1/(14/3) = 3/14 of the work per day
Rate of B and C = 1/(12/5) = 5/12 of the work per day
Rate of C and A = 1/(16/3) = 3/16 of the work per day
So.
⇒ (A + B) + (B + C) + (C + A) = 3/14 + 5/12 + 3/16
⇒ 2(A + B + C) = (3 × 24 + 5 × 28 + 3 × 21)/336
⇒ 2(A + B + C) = (72 + 140 + 63)/336
⇒ 2(A + B + C) = 275/336
⇒ A + B + C = 275/672
Thus,
In 2 days, they can complete in = 275/336