Question 15

A, B and C can complete a task together in 10 days. A and B would need 12 days if only the two of them worked, while B and C would take 20 days if only the two of them worked. If B worked alone, how many days would she take to complete the task?

Solution

A+B+C=10

A+B = 12
B+C = 20

Lcm of (10,12,20) = 120

Efficiency is
A+B = 10
B+C = 6

A+B+C=12

Individual efficiency
A = 12 - 6 = 6
B = 6 - 2=4
C = 12-10 = 2

Individual time taken

$$B=\frac{120}{4}=30$$

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