Question

Two pipes A and B opened simultaneously and they filled a tank in 4 hours. Pipe A fills the tank 15 hours faster than pipe B. How many hours does pipe B alone take to fill the tank?
1. 20 hours
2. 15 hours
3. 17 hours
4. 18 hours

Answer 1

Correct Answer - Option 1 : 20 hours

Given

A and B pipe filled tank in 4 hours

Time taken by A to fill the tank alone = Time taken by pipe B to fill the tank alone - 15

Calculation

Pipe B take x hours to fill the tank

Pipe A takes (x - 15) hours to fill the tank

Tank filled in 1 hour by A = 1/(x - 15)

Tank filled in 1 hour by B = (1/x)

Tank filled in 1 hour by A and B = 1/4

According to question

(1/x) + 1/(x - 15) = 1/4

⇒ (x  - 15 + x)/(x) (x - 15) = 1/4

⇒ 4(2x - 15) = x² - 15x

⇒ 8x - 60 = x² - 15x

⇒ x² - 15x - 8x + 60 = 0

⇒ x²  - 23x + 60 = 0

⇒ x²  - 20x - 3x + 60 = 0

⇒ x(x - 20) - 3(x - 20) = 0

⇒ (x - 3) (x - 20) = 0

⇒ x = 3 and 20

If we take x = 3, then (x - 15) will be negative which is not possible

∴ Time taken by B to fill the tank alone is 20 hours.