Question: A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. What is the time required by the first pipe to fill the tank alone?

1. 6 hours
2. 10 hours
3. 15 hours
4. 30 hours
5. 36 hours

Correct Answer: C

Solution and Explanation:

Approach Solution 1:
Given: The second pipe fills the tank 5 hours faster than the first pipe.
             The second pipe fills the tank 4 hours slower than the third pipe.

Then, second and third pipes will take (x-5) and (x-9) hours respectively to fill the tank.
Given: The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone.
Let’s say the first pipe takes k hours to fill the tank, i.e. in one hour the amount of tank filled is1/k. Similarly we get 1/x - 5 and 1/x - 9 parts of the tank filled in one hour. Hence the relation is

1/x+1/x - 5= 1/x - 9
⇒ x(x - 5)/x (x - 5)= 1/x - 9
⇒(2x - 5)(x - 9)= x(x - 5)
⇒2x^2−5x - 18x + 45= 0
⇒(x - 15)(x - 3)= 0
⇒x = 15.

Approach Solution 2:
Let's Assume First pipe takes A hours , second B and third C

1/A+1/B = 1/C ( as first two pipe take same time as third pipe do)

B=A-5 ( second pipe fills 5 hours faster ) ....1
C=B-4 ( as second pipe is slower than second) ....2

Substituting B in 2

C= A-5 -4
C = A -9
1/A+1/A-5 = 1/A-9

Approach Solution 3:
Suppose the first pipe alone takes x hours to fill the tank.
Then, second and third pipes will take (x-5) and (x-9) hours respectively to fill the tank
It is given that the first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone.

Therefore, 1/x+1/x-5= 1/x-9

⇒ x-5+x/x(x-5)= 1/x-9
⇒(2x-5) (x-9)= x(x-5)
⇒ 2x^2-5x-18x+45= X^2-5X
⇒ x^2-18x+45= 0
⇒ x^2-15x-3x+45= 0
⇒ x(x-15)-3(x-15)= 0
⇒ (x-15) (x-3)= 0
⇒ x= 15 [neglecting x= 3]

So time required by 1st pipe = 15 hours.

“A tank is filled by three pipes with uniform flow. The first two pipes”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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