Question

Pipe A, B, and C together can fill the tank in 30 hours where pipe C can empty the tank in 90 hours then find in how many hours tank will be filled when A and B work together and A, B and C work together alternatively. Starting from when A and B together fills the tank.
1. 88 + 2/3 hours 
2. 89 + 2/3 hours
3. 102 + 2/3 hours
4. 100 + 2/3 hours
5. None of these

Answer 1

Correct Answer - Option 5 : None of these

Given:

A, B, and C can fill the tank in = 30 hours

C can empty the tank in = 90 hours

Calculation:

Total work = 90 unit work

Efficiency	Pipes	Time (in hr)
-1	C	90
3	A+B+C	30
4	A+B	22.5

7 unit work → By pipes (A+B) on 1st hour and (A+B+C) on the 2nd hour → 2 hrs

84 unit work	By pipes (A+B) on 1st hour and (A+B+C) on 2nd hour till 24 hrs	24 hrs
4 unit work	By pipes (A+B)	1 hrs
2 unit work	By pipes (A+B+C)	2/3 hrs
90 unit work		25(2/3) hrs