A and B can do a piece of work in 12 days, B can C in 8 days and C and A in 6 days. How long would B take to do the same work alone?
Explanation
Given:
Time taken by A and B to complete the work = 12 days
Time taken by B and C to complete the work = 8 days
Time taken by C and A to complete the work = 6
Formulae used:
Time = Total work / Efficiency
Calculation:
Let us assume the total work is 1 unit.
⇒ A and B complete 1 unit work in 12 days → (A and B)'s 1 day's work = 1/12
⇒ B and C complete 1 unit work in 8 days → (B and C)'s 1 day's work = 1/8
⇒ A and C complete 1 unit work in 6 days → (A and C)'s 1 day's work = 1/6
Adding everyone's 1 day's work:
⇒2(A+B+C)=(1/12)+(1/8)+(1/6)
⇒A+B+C=9/48
= A, B, and C's 1 day's work = 9/48
⇒ B's 1 day's work = (A+B+C)−(A+C)
⇒ B's 1 day's work =(9/48)−(1/6) = 9-8 x/48 = 1/ 48
⇒ B completes 1/48 of the work in 1 day.
Therefore, B alone will take 48 days to complete the work.
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