A swimming pool is filled by three pipes withuniform flow. The first two pipes operating simultaneously fill the pool inthe same time during which the pool is filled by the third pipe alone. Thesecond pipe fills the pool 5 hours faster than the first pipe and 4 hoursslower than the third pipe. The time required by the first pipe is`6 h r s`b. `10 h r s`c. `15 h r s`d. `30 h r s`

A swimming pool is filled by three pipes withuniform flow. The first t

1.	A swimming pool is filled by three pipes withuniform flow. The first two pipes operating simultaneously fill the pool inthe same time during which the pool is filled by the third pipe alone. Thesecond pipe fills the pool 5 hours faster than the first pipe and 4 hoursslower than the third pipe. The time required by the first pipe is`6 h r s`b. `10 h r s`c. `15 h r s`d. `30 h r s`
Answer» Let `F=x hours``S=x-5 hours``T=x-9 hours`where, F stands for first pipe S for second and T for third pipe`1/x+1/(x-5) =1/(x-9)``(x-5+x)/(x(x+5))= 1/(x-9)``(x-9)(2x-5)=x(x-5)``2x^2-5x-18x + 45= x^2-5x``2x^2-18x+45 = x^2``x^2-18x+45=0``x^2-15x-3x+45=0``x(x-15)-3(x-15)=0``(x-15)(x-3)=0`Therefore,`x=15 or x=3` `x=3 hours` is not possible.Hence, time taken by First pipe, F `=15 hours`then time taken by S `=15-5=10 hours`and by T `=15-9= 6 hours`