Quadratic Equations
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??
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