Question

Two water taps together can fill a tank in  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.​

Answer 1

Answer:

25, 15 hrs

Step-by-step explanation:

let time taken by smaller tap be x hrs

time taken by larger tap=(x-10)hrs

CASE 1

Portion filled in 1 hr=1/x

Portion filled in 75/8 hrs=75/8x

CASE 2

Portion filled in 1 hr=1/(x-10)

Portion filled in 75/8 hrs= 75/8x-80

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

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

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

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

2x-10/x²-10x=8/75

75(2x-10)=8(x²-10x)

150x-750=8x²-80x

8x²-80x-150x+750=0

8x²-230x+750=0

2(4x²-115x+375)=0

4x-115x+375=0

4x-100x-15x+375=0

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

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

x= 25, 15/4

Smaller Tap= x= 25hrs

Larger Tap= x-10= 25-10= 15 hrs