Question

Two water
taps together
fill a tank in 9x3/8 hours
the
tap of
larger
diameter takes l0 hours less than
Smaller one
time in which each top
tank seperately. find the
time in which each tap can separately fill the
tank
​

Answer 1

Answer: Larger diameter of the tap can the tank 15 hours and smaller diameter of the tank can fill the tank in 25 hours.

Step to step explanation: Let the larger diameter tap fills the tank alone in (x – 10) hours.

In 1 hour, the smaller diameter tap can fill 1/x part of the tank.

In 1 hour, the larger diameter tap can fill 1/(x – 10) part of the tank.

Two water taps together can fill a tank in 75 / 8 hours.

But in 1 hour the taps fill 8/75 part of the tank.

1 / x  +  1 / (x – 10) = 8 / 75.

( x – 10 + x ) / x ( x – 10) =  8 / 75.

2( x – 5) / ( x2 – 10 x) = 8 / 75.

4x2 – 40x = 75x – 375.

4x2 – 115x + 375 = 0

4x2 – 100x – 15x + 375 = 0

4x ( x – 25) – 15( x – 25) = 0

( 4x -15)( x – 25) = 0.

x = 25, 15/ 4.

But x = 15 / 4 then x – 10 = -25 /4 which is not possible since time

But x = 25 then x – 10 = 15.

I hope this answer is helpful for you.

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let the time taken by smaller tap be x hr.

And the time taken by larger tap be (x - 10) hr.

Part  filled by a smaller tap in 1 hour = 1/x

Part  filled by a larger tap in 1 hour = 1/x - 10

According to the Question,

⇒ 1/x + 1/(x - 10) = 8/75

⇒ x - 10 + x/x(x - 10) = 8/75

⇒ 2x - 10/x(x - 10) = 8/75

⇒ 75(2x - 10) = 8(x² + 10x)

⇒ 150x - 750 = 8x² + 80x

⇒ 8x² - 230x - 750 = 0

⇒ 8x² - 200x - 30x + 750 = 0

⇒ 8x(x - 25) - 30(x - 25) = 0

⇒ (x - 25) (8x - 30) = 0

⇒ x = 25, - 30/8 (As x can't be negative)

⇒ x = 25

Time taken by smaller tap = x = 25 hours.

Time taken by larger tap = x - 10 = 25 - 10 = 15 hours.