Three pipes X, Y and Z can fill a pot in 6 hours. After working togeth

1.	Three pipes X, Y and Z can fill a pot in 6 hours. After working together for two hours, pipe Z is closed and pipe X and pipe Y fill the pot in 8 hours. In how much time the pot can be filled by pipe Z alone?1. 102. 123. 84. 9
Answer» Correct Answer - Option 2 : 12 Given: Three pipes X, Y and Z can fill a pot in 6 hours Concept: If a tap can fill a tank in x hours, then the tank filled by the tap in 1 hour = 1/x of the total tank. Calculation: Part of the pot filled by (X + Y + Z) in 1 hours = \(\frac{1}{6}\) Part of the pot filled by these in 2 hours = \(\frac{2}{6}{\rm{}} = {\rm{}}\frac{1}{3}\) Remaining part = \(1 - \frac{1}{3}{\rm{}} = {\rm{}}\frac{2}{3}\) Time taken by X and Y in filling \(\frac{2}{3}\)rd part = 8 hours Time taken by X and Y in filling the whole pot = \(\frac{{8\; \times \;3}}{2}\) = 12 hours Part of pot filled by Z in an hour ⇒ \(\frac{1}{6} - \frac{1}{{12}} = \frac{1}{{12}}\) ∴ The required time is 12 hours.

Three pipes X, Y and Z can fill a pot in 6 hours. After working together for two hours, pipe Z is closed and pipe X and pipe Y fill the pot in 8 hours. In how much time the pot can be filled by pipe Z alone?1. 102. 123. 84. 9

Answer» Correct Answer - Option 2 : 12

Given:

Three pipes X, Y and Z can fill a pot in 6 hours

Concept:

If a tap can fill a tank in x hours, then the tank filled by the tap in 1 hour = 1/x of the total tank.

Calculation:

Part of the pot filled by (X + Y + Z) in 1 hours = \(\frac{1}{6}\)

Part of the pot filled by these in 2 hours = \(\frac{2}{6}{\rm{}} = {\rm{}}\frac{1}{3}\)

Remaining part = \(1 - \frac{1}{3}{\rm{}} = {\rm{}}\frac{2}{3}\)

Time taken by X and Y in filling \(\frac{2}{3}\)rd part

= 8 hours

Time taken by X and Y in filling the whole pot

= \(\frac{{8\; \times \;3}}{2}\) = 12 hours

Part of pot filled by Z in an hour

⇒ \(\frac{1}{6} - \frac{1}{{12}} = \frac{1}{{12}}\)

∴ The required time is 12 hours.