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# Two water taps together can fill a tank in 9 and 3/8 hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

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## Exercise 4.3

Two water taps together can fill a tank in 9 and 3/8 hours. The tap of larger diameter takes 10 hour less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank??

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1. Let the time taken by larger tap (A )= x hours

Time taken by smaller tap  (B)= (x-10) h

Time taken by both taps (A+B)= 9and 3/8 hours = 75/8 h

According to the question

A’s one hour work+ B’s one hour work = (A+B)’s one hour work

1/x+ 1/(x-10) = 8/75

Taking LCM, and cross multiplying

75(2x-10) = 8( x²- 10x)

150x – 750 = 8x² – 80x

75x – 375 = 4x² – 40x ( dividing by 2)

4x² -115x +375 = 0

4x²- 100x-15x+375= 0

(4x-15)(x-25)= 0

∴ x= 15/4 and x= 25

Value of x can’t be 15/4(3.75) because the other tap takes 10h less than this which is not possible

∴ larger tap takes 25 h

And smaller takes 15 h

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