Question

a tank can be filled up by 6hours.the smaller tap alone takes 5 hours more than the bigger tab alone. find the time required by each tap to fill the tank separately​

Answer 1

Answer:

the small tap fills the tank in 15 hours and the large tap fills the tank in 10 hours. (Answer)

Step-by-step explanation:

Let the large tap takes x hours to fill up the tank alone.

Then, in 1 hour the large tap fills the part of the tank.

So, as per the given condition, the small tap will fill the tank alone in (x + 5) hours.

Then, in 1 hour the large tap fills the part of the tank.

When both of them are open then in 1 hour they will fill part of the tank.

Given that, both the taps when open they fill the tank in 6 hours.

So, when both the tanks are open they will fill part of the tank in 1 hour.

Therefore, we can write the equation as

⇒ 6(2x + 5) = x(x + 5)

⇒ x² - 7x - 30 = 0

⇒ x² - 10x + 3x - 30 = 0

⇒ (x - 10)(x + 3) = 0

So, x = 10 hours {As x can not be negative}

So, x + 5 = 15 hours.

Therefore, the small tap fills the tank in 15 hours and the large tap fills the tank in 10 hours. (Answer)

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