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 x2 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(a2 + 5a)
⇒ 200a + 500 = 9a2 + 45a
⇒ 9a2 – 155a - 500 = 0
⇒ 9a2 – 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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