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kavana73:
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let assume smaller tap can fill tank in x hours
then larger tab will fill tank in x-10 hours
in 1 hour smaller tap alone can fill = 1/x part of tank
in 1 hour larger tap alone can fill = 1/(x-10) part of tank
in 1 hour both can fill = 1/x + 1/(x-10) part of tank
given
in 75/8 hour both fill = full tank
in 1 hour both will fill = 1/(75/8) = 8/75 part of tank
equating both
1/x + 1/(x-10) = 8/75
(x-10+x)/(x^2-10x) = 8/75
(x-10 + x) × 75 = 8×^2 - 80x
150x - 750 = 8x^2 -80x
8x^2 -80x -150x + 750 = 0
8x^2 - 230x + 750 =0
4x^2 - 115x + 375 =0
4x^2 - 100x - 15x + 375 =0
4x( x - 25) -15(x - 25) = 0
(4x -15)(x -25)=0
x = 15/4, x =25
x = 15/4 is not valid as x - 10 will go negative
so x =25
larger tap time = x - 10 = 25-10 = 15
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