##### Ritesh

#### Question

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**Question**

18-09-05

**Answer**

Q. Two pipe can fill a cistern in 14 and 16 hours respectively the pipe are opened together and it is found that due to leakage in the bottom of cistern, it takes 32 minutes more to filled up . When the cistern is full , what time will the leak take to empty it .

**Solution**

Work Done by Cistern to fill tank in one hour =1/14+1/16=15/112

Time take by Cistern to fill tank =112/15=7 hour 28 minutes

As the leakage took place both will take 32 minutes more

Total time taken=7 hour28 minutes+32 minutes =8 hours

Now Work done by both pipe and leakage 1 hour =1/8

Work done by leakage 1 hour=15/112-1/8=1/112

Time to empty cistern =112 minutes

**Short Cut**

A=14 B=16 Total work will be LCM (14,16= 112)

A=14 A’s 1 hour work =112/14= 8

B=16 B’s 1 hour work=112/16=7

Time Taken by A and B will be = 112/8+7=112/15

Total Time will be (112/15)+32(leakage time)= 8 hours

Work done to empty tank =15/112-1/8= 1/112

Time will be =112