A cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 8 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled? a)4.8 hrb)2.4 hrc)3.6 hrd)1.8 hrCorrect answer is option 'A'. Can you explain this answer?

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A cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 8 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?

a)
4.8 hr
b)
2.4 hr
c)
3.6 hr
d)
1.8 hr

Correct answer is option 'A'. Can you explain this answer?

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Test: Pipes And Cistern- 1

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A cistern can be filled by a tap in 3 hours while it can be emptied by...

Given:
- Time taken to fill the cistern by one tap = 3 hours
- Time taken to empty the cistern by another tap = 8 hours

To find:
- Time taken to fill the cistern when both taps are opened simultaneously

Explanation:
Let's assume that the capacity of the cistern is C liters.
Let's also assume that the rate of filling the cistern is R liters per hour.

Rate of filling by the first tap:
- The first tap fills the cistern in 3 hours.
- Therefore, the rate of filling by the first tap = C/3 liters per hour.

Rate of emptying by the second tap:
- The second tap empties the cistern in 8 hours.
- Therefore, the rate of emptying by the second tap = C/8 liters per hour.

Total rate when both taps are opened simultaneously:
- When both taps are opened simultaneously, the net rate of filling the cistern can be calculated by subtracting the rate of emptying from the rate of filling.
- Net rate = (C/3) - (C/8) liters per hour

Time taken to fill the cistern:
- Time taken to fill the cistern can be calculated by dividing the total capacity of the cistern by the net rate of filling.
- Time taken = C / [(C/3) - (C/8)] hours

Simplifying the expression:
- Taking the LCM of 3 and 8, we get 24 as the denominator.
- Time taken = C / [(8C - 3C) / 24]
= C / [(5C) / 24]
= 24C / 5C
= 24/5 hours
= 4.8 hours

Conclusion:
Therefore, the cistern will get filled in 4.8 hours when both taps are opened simultaneously. Hence, the correct answer is option 'A' (4.8 hr).

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A cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 8 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled? a)4.8 hrb)2.4 hrc)3.6 hrd)1.8 hrCorrect answer is option 'A'. Can you explain this answer?

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