Find the appropriate relation for quantity 1 and quantity 2 in the following question:

An artificial kund is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the kund at the same time during which the kund is filled by the third pipe alone. The second pipe fills the kund 5 hours faster than the first pipe and 4 hours slower than the third pipe.

Quantity 1: The time required by the first pipe?

Quantity 2: Time taken by all three pipes to fill the Kund simultaneously

A) Quantity 1 > Quantity 2	B) Quantity 1 ≥ Quantity 2
C) Quantity 1 < Quantity 2	D) Quantity 1 ≤ Quantity 2

Answer: A) Quantity 1 > Quantity 2

Explanation:

Quantity 1:
Let the first pipe alone takes x hours to fill the
tank.
⇒The second and third pipes will take (x-5) and
(x-9) hours respectively.
According to the given information:
∴ $\frac{1}{x - 9}$

⇒ (x-9)(2x-5) = x2 – 5x
⇒ 2x2 – 5x – 18x + 45 = x2 – 5x
⇒ x
2 -18x + 45 = 0
⇒ (x-15) (x-3) = 0
⇒ x = 15, 3

The first pipe can take 15 hours to fill the kund.
∵ 3 hours doesn’t satisfy the statement.
Quantity 2:
∴ Time taken by second pipe = x-5
⇒ Time taken by second pipe = 15-5 = 10hours
∴ Time taken by third pipe = x -9
⇒ Time taken by third pipe = 15- 9 = 6 hours
Now,

Net part filled in 1 hour = $\frac{1}{15} + \frac{1}{10} + \frac{1}{6}$
⇒ Net part filled in 1 hour = $\frac{4 + 6 + 10}{60}$
⇒Net part filled in 1 hour = $\frac{20}{60} = \frac{1}{3}$
∴The Kund will be full in 3/1 hours if all the pipes are opened simultaneously
Now, comparing
15 > 3
Thus, Quantity 1 > quantity 2

Subject: Quantitative Aptitude - Arithmetic Ability
Exam Prep: Bank Exams , GATE
Job Role: Bank Clerk , Bank PO