Shortcut Trick
Time taken by both pipes to fill the whole tank = (12 × 36) ÷ (12 + 36)
Time taken for whole tank = 432 ÷ 48 = 9 hours
To fill one-third of the tank, the time required is simply 1/3 of the total time.
Required time = 9 × (1/3) = 3 hours
∴ The correct answer is 3 hours.
Alternate Method
Given:
Time taken by Pipe X to fill the tank = 12 hours
Time taken by Pipe Y to fill the tank = 36 hours
| Pipe | Hours | Total Work | Efficiency |
|---|
| X | 12 | 36 | 3 |
| Y | 36 | 1 | |
Calculations:
⇒ Total capacity of the tank (Total Work) = 36 units
⇒ Combined efficiency of Pipe X and Pipe Y = 3 + 1 = 4 units/hour
⇒ We need to find the time to fill one-third part of the tank.
⇒ Required work = 36 × (1/3) = 12 units
⇒ Time required = Required work ÷ Combined efficiency
⇒ Time required = 12 ÷ 4 = 3 hours
∴ The correct answer is 3 hours.
Additional Information
Two Pipes Filling a Tank
If pipe A fills a tank in x hours and pipe B fills it in y hours, total time taken together = (x × y) ÷ (x + y) hours.
One Filling and One Emptying Pipe
If pipe A fills in x hours and pipe B empties in y hours (where y > x), time taken to fill = (x × y) ÷ (y − x) hours.
Part of Tank Filled
To fill a specific fraction of the tank, simply multiply the total time taken to fill the entire tank by that fraction.