Question

Two pipes P and Q would fill an empty cistern in 24 min respectively .Both the pipes being opened together ,find when the first pipe must be turned off so that the empty cistern may be just fitted in 16 min.

Help me.

Answer 1

Fraction of cistern P = 1/24

Fraction of cistern Q = 1/32

Lcm..... = 4+3/96 = 7/96

Let it be 7x/96

7x/96+1/32×(16-x) = 1

Therefore no. Of minute pipe opened = (16-x)

7x-3x/96+16/32= 1

4x/96+16/32 = 1

x/24+1/2= 1

x+12/24=1

x+12 = 24

x = 12

After 12 minute we turn off the first pipe