Question

A, B and C can complete a piece of work in 12, 20 and 15 days, respectively. A, B and C will complete the work while working on alternate days. C works on the 1st day, B works on the 2nd day and A works on the 3rd day and so on. In how many days will the work get complete?

• A. 24
• B. 15
• C. 30
• D. 12

Answer 1

Answer:

B. 15

Work rates per day:

• A → ( \frac{1}{12} )

• B → ( \frac{1}{20} )

• C → ( \frac{1}{15} )

They work in a cycle of 3 days: C → B → A

Work done in 3 days

$\frac{1}{15} + \frac{1}{20} + \frac{1}{12}$

LCM of 15, 20, 12 = 60

$= \frac{4 + 3 + 5}{60} = \frac{12}{60} = \frac{1}{5}$

So, in 3 days → 1/5 work is done

Work done in 15 days (5 cycles)

$5 \times \frac{1}{5} = 1$

$\boxed{15 \text{ days}}$