Three pipes X, Y, Z can fill an overhead pot in 4, 6 and 12 hours resp

1.	Three pipes X, Y, Z can fill an overhead pot in 4, 6 and 12 hours respectively. How long would the three pipes take to fill the pot, if all of them are open together?1. 2 hrs.2. 4 hrs.3. 3 hrs.4. 5 hrs.
Answer» Correct Answer - Option 1 : 2 hrs. Given: Three pipes X, Y, Z can fill an overhead pot in 4, 6 and 12 hours respectively 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 all three pipes in an hours ⇒ \(\frac{1}{4}{\rm{}} + {\rm{}}\frac{1}{6}{\rm{}} + {\rm{}}\frac{1}{{12}}{\rm{}} = {\rm{}}\frac{{6{\rm{\;}} + {\rm{\;}}4{\rm{\;}} + {\rm{\;}}2}}{{24}}{\rm{}} = {\rm{}}\frac{1}{2}\) ∴ The pot will be filled in 2 hours.

Three pipes X, Y, Z can fill an overhead pot in 4, 6 and 12 hours respectively. How long would the three pipes take to fill the pot, if all of them are open together?1. 2 hrs.2. 4 hrs.3. 3 hrs.4. 5 hrs.

Answer» Correct Answer - Option 1 : 2 hrs.

Given:

Three pipes X, Y, Z can fill an overhead pot in 4, 6 and 12 hours respectively

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 all three pipes in an hours

⇒ \(\frac{1}{4}{\rm{}} + {\rm{}}\frac{1}{6}{\rm{}} + {\rm{}}\frac{1}{{12}}{\rm{}} = {\rm{}}\frac{{6{\rm{\;}} + {\rm{\;}}4{\rm{\;}} + {\rm{\;}}2}}{{24}}{\rm{}} = {\rm{}}\frac{1}{2}\)

∴ The pot will be filled in 2 hours.

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