14. two pipes a and b together can fill a cistern in 4 hours. Had they been opened separately, then b would have taken 6 hours more than a to fill the cistern. How much time will be taken by a to fill the cistern separately?
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1/A+ 1/B =1/4
let A can fill it in X hours
B can.............. X+6
1/X +1/X+6 =1/4
(X+6 +X)/{(X+6)×X }= 1/4
2X+6 /X^2 +6X =1/4
8X+24 = X^2 +6X
X^2-2X-24 =0
X^2 -6X+4X-24=0
(X-6)(X+4) =0
time can't be negative so,
X=6
So A can fill the Cistern in 6 hour.
let A can fill it in X hours
B can.............. X+6
1/X +1/X+6 =1/4
(X+6 +X)/{(X+6)×X }= 1/4
2X+6 /X^2 +6X =1/4
8X+24 = X^2 +6X
X^2-2X-24 =0
X^2 -6X+4X-24=0
(X-6)(X+4) =0
time can't be negative so,
X=6
So A can fill the Cistern in 6 hour.
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