Question

Three pipes A, B, C can fill a cistern in 9 hours ,12 hours and 18 hours respectively. if pipe A is open all the time and B and C are opened alternatively for one hour each then the cistern will be full in?
1. 4.5 hours 
2. 5.5 hours
3. 4 hours 
4. 5 hours
5. 6 hours

Answer 1

Correct Answer - Option 2 : 5.5 hours

GIVEN:

time taken by pipe A = 9 hours

​time taken by pipe B = 12 hours

​time taken by pipe C = 18 hours

EXPLANATION:

let the capacity of tank be 36 (L.C.M of 9, 12, 18)

the efficiency of pipe A per hour = \(\frac{36}{9}\) = 4

the efficiency of pipe B per hour = \(\frac{36}{12}\) = 3

the efficiency of pipe C per hour = \(\frac{36}{18}\) = 2

part filled by A and B in one hour = 4 + 3 = 7

part filled by A and C in one hour = 4 + 2 = 6

part filled in 2 hours = 7 + 6 = 13

part filled in 4 hours = 26

remaining part = 36 - 26 = 10

part filled in 5th hour by A and B = 7

remaining 3 parts will be filled by A and C in half an hour

∴ Total time = 5.5 hours