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Three taps A B and C fill a cistern in 10 minutes,12 minutes and 15 minutes respectively. They all are together turned on but after 5 /2 minutes B and C are turned off . How much time will A take to fill the cistern.
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Let capacity of cistern=x
So in 1min A can fill x/10,B can fill x/12,and C can fill x/15
Let y be the longer time taken by A and B to fill the tank
=>(x/10+x/12)x(5/2+y) +(x/15) 5/2=x
=>(12x+10x/120)x(5+2y/y)+x/6=x
=>(22x/120)(5+2y/y)=x-x/6
=>(11x/60)(5+2y/y)=5x/6
=>5+2y/y=(5x/6)(60/11x)
=>5+2y/y=300/66
=>5+2y/y=50/11
=>55+22y=50y
=>28y=55
=>y=55/28
=>1.96min
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