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A tap can fill storage in 8 hours and another tap can discharge it in 16 hours. In the event that both the taps are open, the time taken to fill the tank will be:
- a)8 hours
- b)10 hours
- c)16 hours
- d)24 hours
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A tap can fill storage in 8 hours and another tap can discharge it in ...
Net part filled in 1 hr = (1/8 ? 1/16) = 1/16
Total time taken to fill the tank = 16 hrs.
Total time taken to fill the tank = 16 hrs.
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Community Answer
A tap can fill storage in 8 hours and another tap can discharge it in ...
Understanding the Problem
In this scenario, we have two taps: one that fills a tank and another that empties it.
Details of the Taps
- Filling Tap: Fills the tank in 8 hours.
- Discharging Tap: Empties the tank in 16 hours.
Calculating Rates of Work
- Filling Rate: The filling tap can fill 1 tank in 8 hours, which means it fills 1/8 of the tank in one hour.
- Discharging Rate: The discharging tap can empty 1 tank in 16 hours, meaning it empties 1/16 of the tank in one hour.
Combined Rate of Work
To find the combined effect of both taps working together, we add their rates:
- Net Filling Rate = Filling Rate - Discharging Rate
- Net Filling Rate = 1/8 - 1/16
Finding a Common Denominator
To perform this operation, we convert the fractions:
- 1/8 = 2/16
Now we can subtract:
- Net Filling Rate = 2/16 - 1/16 = 1/16
Time Taken to Fill the Tank
To find the time taken to fill the tank when both taps are open:
- If the net filling rate is 1/16 of the tank per hour, it will take 16 hours to fill 1 full tank.
Final Conclusion
Thus, when both taps are open, the time taken to fill the tank is 16 hours, confirming that option 'C' is correct.
In this scenario, we have two taps: one that fills a tank and another that empties it.
Details of the Taps
- Filling Tap: Fills the tank in 8 hours.
- Discharging Tap: Empties the tank in 16 hours.
Calculating Rates of Work
- Filling Rate: The filling tap can fill 1 tank in 8 hours, which means it fills 1/8 of the tank in one hour.
- Discharging Rate: The discharging tap can empty 1 tank in 16 hours, meaning it empties 1/16 of the tank in one hour.
Combined Rate of Work
To find the combined effect of both taps working together, we add their rates:
- Net Filling Rate = Filling Rate - Discharging Rate
- Net Filling Rate = 1/8 - 1/16
Finding a Common Denominator
To perform this operation, we convert the fractions:
- 1/8 = 2/16
Now we can subtract:
- Net Filling Rate = 2/16 - 1/16 = 1/16
Time Taken to Fill the Tank
To find the time taken to fill the tank when both taps are open:
- If the net filling rate is 1/16 of the tank per hour, it will take 16 hours to fill 1 full tank.
Final Conclusion
Thus, when both taps are open, the time taken to fill the tank is 16 hours, confirming that option 'C' is correct.
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