9) A & B can do a piece of work in 72 days, B & C can do it in 120 days and A & C can do in in 90 days. In how many days all three together can do the work?

To solve this problem, we first need to find the rate at which A, B, and C work.

Step 1: Find the rate of work for A & B, B & C, and A & C.

The rate of work is the reciprocal of the time taken to complete the work. So,

• The rate of work for A & B = 1/72 work/day
• The rate of work for B & C = 1/120 work/day
• The rate of work for A & C = 1/90 work/day

Step 2: Add the rates of work for A & B, B & C, and A & C.

The total rate of work for A & B, B & C, and A & C = 1/72 + 1/120 + 1/90 = 1/30 work/day

Step 3: Divide the total rate of work by 2 to find the rate of work for A, B, and C together.

The rate of work for A, B, and C together = 1/30 ÷ 2 = 1/60 work/day

Step 4: Find the time taken by A, B, and C to complete the work.

The time taken is the reciprocal of the rate of work. So, the time taken by A, B, and C to complete the work = 1 ÷ (1/60) = 60 days.

So, all three together can do the work in 60 days.