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 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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