Q. 734.6( 12 Votes )

To fill a s

Answer :

Let the larger diameter pipe fill it in ‘a’ hours


The smaller diameter pipe fills it in ‘a + 10’ hours


In 1 hour, larger diameter pipe fills 1/a part of the pool.


In 1 hour, smaller diameter pipe fills 1/(a + 10) part of the pool.


Given, the pipe of larger diameter used for 4 hours and the pipe of smaller diameter for 9 hours, only half of the pool can be filled.


4 × 1/a + 9 × 1/(a+10) = 1/2


2(4a + 40 + 9a) = a2 + 10a


26a + 80 = a2 + 10a


a2 – 16a – 80 = 0


a2 – 20a + 4a – 80 = 0


a(a – 20) + 4(a – 20) = 0


(a + 4)(a – 20) = 0


a = 20 hours


Time in which smaller diameter pipe fills the pool = 20 + 10 = 30 hours

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses