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Two taps A and B can fill a tank in 10 hours and 15 hours, respectively. If both the taps are opened together the tank will be full in ______
- a)8 hours
- b)6 hours
- c)5 hours
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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Given:
Tap A can fill the tank in 10 hours.
Tap B can fill the tank in 15 hours.
To find:
The time taken to fill the tank when both taps A and B are opened together.
Solution:
Let's assume that the tank has a capacity of 1 unit.
The filling rate of tap A is 1/10 units per hour.
The filling rate of tap B is 1/15 units per hour.
When both taps A and B are opened together, their filling rates are added.
So, the combined filling rate of tap A and B is (1/10) + (1/15) units per hour.
To find the time taken to fill the tank when both taps are opened together, we can use the formula:
Time = Tank capacity / Combined filling rate
Substituting the given values:
Time = 1 / [(1/10) + (1/15)]
Calculating the combined filling rate:
To add the fractions (1/10) and (1/15), we need to find a common denominator.
The least common multiple (LCM) of 10 and 15 is 30.
So, (1/10) + (1/15) = (3/30) + (2/30) = 5/30
Calculating the time:
Time = 1 / (5/30)
= 1 * (30/5)
= 30/5
= 6 hours
Therefore, when both taps A and B are opened together, it will take 6 hours to fill the tank. Hence, the correct answer is option B.
Tap A can fill the tank in 10 hours.
Tap B can fill the tank in 15 hours.
To find:
The time taken to fill the tank when both taps A and B are opened together.
Solution:
Let's assume that the tank has a capacity of 1 unit.
The filling rate of tap A is 1/10 units per hour.
The filling rate of tap B is 1/15 units per hour.
When both taps A and B are opened together, their filling rates are added.
So, the combined filling rate of tap A and B is (1/10) + (1/15) units per hour.
To find the time taken to fill the tank when both taps are opened together, we can use the formula:
Time = Tank capacity / Combined filling rate
Substituting the given values:
Time = 1 / [(1/10) + (1/15)]
Calculating the combined filling rate:
To add the fractions (1/10) and (1/15), we need to find a common denominator.
The least common multiple (LCM) of 10 and 15 is 30.
So, (1/10) + (1/15) = (3/30) + (2/30) = 5/30
Calculating the time:
Time = 1 / (5/30)
= 1 * (30/5)
= 30/5
= 6 hours
Therefore, when both taps A and B are opened together, it will take 6 hours to fill the tank. Hence, the correct answer is option B.
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Two taps A and B can fill a tank in 10 hours and 15 hours, respectively. If both the taps are opened together the tank will be full in ______a)8 hours b)6 hoursc)5 hours d)None of theseCorrect answer is option 'B'. Can you explain this answer?
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