When operated separately, pipe A takes 5 hours less than pipe B to fil

1.	When operated separately, pipe A takes 5 hours less than pipe B to fill a cistern, and when both pipes are operated together, the cistern gets filled in 6 hours. In how much time (in hours) will pipe B fill the cistern, if operated separately?1. 92. 103. 154. 18
Answer» Correct Answer - Option 3 : 15 Given: Pipe A takes 5 hours less than pipe B to fill a cistern. Time to fill the tank by pipe A and B together = 6 hours Formula used: Efficiency = Total work/total time Concept used: Let time to fill the whole tank by pipe B alone be x hours. So, time to fill the whole tank by pipe A will be (x - 5) hours. Let capacity of total tank be 6x(x - 5) units. Efficiency of pipe A = 6x(x - 5)/(x - 5) ⇒ 6x units/hour Efficiency of pipe B = 6x(x - 5)/x ⇒ 6(x - 5) units/hour Efficiency of A and B together = 6x(x - 5)/6 ⇒ x(x - 5) units/hour Equating combined efficiency, 6x + 6(x - 5) = x(x - 5) ⇒ 6x + 6x - 30 = x² - 5x ⇒ 12x - 30 = x² - 5x ⇒ x² - 5x - 12x + 30 = 0 ⇒ x² - 17x + 30 = 0 ⇒ (x - 15)(x - 2) = 0 Taking (x - 15) = 0 ⇒ x = 15 hours ∴ Pipe B will fill the cistern in 15 hours.

When operated separately, pipe A takes 5 hours less than pipe B to fill a cistern, and when both pipes are operated together, the cistern gets filled in 6 hours. In how much time (in hours) will pipe B fill the cistern, if operated separately?1. 92. 103. 154. 18

Answer» Correct Answer - Option 3 : 15

Given:

Pipe A takes 5 hours less than pipe B to fill a cistern.

Time to fill the tank by pipe A and B together = 6 hours

Formula used:

Efficiency = Total work/total time

Concept used:

Let time to fill the whole tank by pipe B alone be x hours.

So, time to fill the whole tank by pipe A will be (x - 5) hours.

Let capacity of total tank be 6x(x - 5) units.

Efficiency of pipe A = 6x(x - 5)/(x - 5)

⇒ 6x units/hour

Efficiency of pipe B = 6x(x - 5)/x

⇒ 6(x - 5) units/hour

Efficiency of A and B together = 6x(x - 5)/6

⇒ x(x - 5) units/hour

Equating combined efficiency,

6x + 6(x - 5) = x(x - 5)

⇒ 6x + 6x - 30 = x² - 5x

⇒ 12x - 30 = x² - 5x

⇒ x² - 5x - 12x + 30 = 0

⇒ x² - 17x + 30 = 0

⇒ (x - 15)(x - 2) = 0

Taking (x - 15) = 0

⇒ x = 15 hours

∴ Pipe B will fill the cistern in 15 hours.