Question

A and B can do a work in 12 days, B and C can do the same work in 15 days, and C and A can do the same work in 20 days. A, B and C will complete the work together in:

• A. 8 days
• B. 15 days
• C. 20 days
• D. 10

Answer 1

Answer:

D. 10

Let the amount of work done by A, B, and C in one day be a, b, and c respectively.

1. Given Information:

   • A and B together can complete the work in 12 days. This means their combined work rate is 1/12 per day. So, a + b = 1/12.

   • B and C together can complete the work in 15 days. Their combined work rate is 1/15 per day. So, b + c = 1/15.

   • C and A together can complete the work in 20 days. Their combined work rate is 1/20 per day. So, c + a = 1/20.

2. Finding the Combined Work Rate of A, B, and C:

   • Add the three equations: (a + b) + (b + c) + (c + a) = 1/12 + 1/15 + 1/20

   • This simplifies to 2(a + b + c) = (5 + 4 + 3) / 60 = 12/60 = 1/5.

   • Therefore, the combined work rate of A, B, and C is (1/5) / 2 = 1/10 per day.

3. Calculating the Time Taken Together:

   • If their combined work rate is 1/10 of the work per day, they will complete the entire work in the reciprocal of this rate.

   • Time taken = 1 / (1/10) = 10 days.