Question

Three taps X, Y and Z can fill a tanker in 6 hours. After working together for 2 hours, tap Z is closed and tap X and tap Y takes 7 hours more to fill it. What will be the time taken by tap Z alone to fill the tanker?
1. 14 hours
2. 15 hours
3. 16 hours
4. 17 hours

Answer 1

Correct Answer - Option 1 : 14 hours

Given:

Three taps X, Y and Z can fill a tanker in 6 hours

After working together for 2 hours, tap Z is closed and tap X and tap Y takes 7 hours more to fill it.

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 tanker filled by taps X, Y and Z in 1 hr = \(\frac{1}{6}\)

Part of the tanker filled by all three taps in 2 hours = \(\frac{1}{3}\)

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

Now, tap X and Y fill 2/3 parts of the tanker in 7 hours

Tap X and Y will fill the tanker in \(\frac{{7\; \times \;3}}{2}{\rm{}} = {\rm{}}\frac{{21}}{2}\) hours

Part of the tanker filled by X and Y in 1 hour = \(\frac{2}{{21}}\)

Part of the tanker filled by Z in 1 hour = \(\frac{1}{6} - \frac{2}{{21}}\)

⇒ \(\frac{{7 \;- \;4}}{{42}}{\rm{}} = {\rm{}}\frac{1}{{14}}\)

∴ Tap Z will fill the tanker in 14 hours.