Q. 204.6( 5 Votes )

# Two pipes running together can fill a tank in minutes. If one pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each pipe would fill the tank separately.

Answer :

Let the faster pipe fill the tank in ‘a’ min.

**Given:** Slower pipe fills it in ‘a + 5’ min.

**To find:** Time taken by each pipe.

**Method Used:**

To solve the quadratic equation by factorisation method, follow the steps:

1) Multiply the coefficient of x^{2} and constant term.

2) factorise the result obtained in step 1.

3) Now choose the pair of factors in such a way that after adding or subtracting(splitting) them

You get coefficient of x.

**Explanation:**

The faster pipe fills the tank in ‘a’ min.

Slower pipe fills it in ‘a + 5’ min.

Given, the pipes running together can fill a tank in

In 1 min, part of tank filled

The faster pipe fills in 1 min

The slower pipe fills in 1 min

According to the question,

⇒ 100(a + a + 5) = 9(a^{2} + 5a)

⇒ 200a + 500 = 9a^{2} + 45a

⇒ 9a^{2} – 155a - 500 = 0

⇒ 9a^{2} – 180a + 25a - 500 = 0

⇒ 9a (a – 20) + 25(a – 20) = 0

⇒ (9a + 25) (a – 20) = 0

⇒ a = 20 mins

Slower pipe will fill it in a+5 = 25 min

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