Question

Two water taps together can fill a tank in 15/8 hours. The tap with
larger diameter takes two hours less than the tap with smaller one to
fill the tank separately. Find the time in which each tap can fill the tank
separately.​

Answer 1

Let there be two taps A and B and let A be the tap with longer diameter than tap B then  

A.T.Q tap A takes 2 hours less than tap B if tap B is taking X hours then Tap A would take (X-2) hours  

Now,1/x + 1/(x-2) = 8/15

= x-2 + x / x^2-2x =8/15 = (2x-2 )15 = 8(x^2-2x)= 30x - 30 = 8x^2 - 16x8x^2-16x-30x+30= 08x^2 -46x +30 = 08x^2 -40x-6x +30 = 08x(x-5) -6(x-5) = 0X=5 or X=6/8  

If x=3/4....(as 6/8 = 3/4)

Then time taken by tap A that is x-2 would negative Hence tap B take 5hours where as tap A takes ( 5-2 ) hours i.e 3 hours Answers...... Hope this will help you all