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Two pipes A and B can fill a tank in 36 hours and 45 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?
- a)20 hours
- b)30 hours
- c)15 hours
- d)25 hours
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Two pipes A and B can fill a tank in 36 hours and 45 hours respectivel...
Part filled by A in 1 hour = (1/36); Part filled by B in 1 hour = (1/45);
Part filled by (A + B) In 1 hour =(1/36)+(1/45)=(9/180)=(1/20)
Hence, both the pipes together will fill the tank in 20 hours.
Part filled by (A + B) In 1 hour =(1/36)+(1/45)=(9/180)=(1/20)
Hence, both the pipes together will fill the tank in 20 hours.
Most Upvoted Answer
Two pipes A and B can fill a tank in 36 hours and 45 hours respectivel...
To find out how much time will be taken to fill the tank when both pipes A and B are opened simultaneously, we need to calculate their combined rate of filling the tank.
Let's assume that the tank has a capacity of 1 unit.
Rate of filling by pipe A: 1/36 units per hour
Rate of filling by pipe B: 1/45 units per hour
Since the rates are given in units per hour, we can add them to get the combined rate:
Combined rate = 1/36 + 1/45
To add these fractions, we need to find a common denominator, which is the least common multiple (LCM) of 36 and 45. The LCM of 36 and 45 is 180.
So, let's rewrite the fractions with a common denominator of 180:
Combined rate = (180/36) + (180/45)
= 5 + 4
= 9 units per hour
Therefore, when both pipes A and B are opened simultaneously, they fill the tank at a rate of 9 units per hour.
Now, we can find the time taken to fill the tank by dividing the tank's capacity (1 unit) by the combined rate (9 units per hour):
Time taken = 1/9 hours
Since the question asks for the time taken in hours, we can convert the fraction to hours:
1/9 hours = (1/9) * 60 minutes
= 6.67 minutes (rounded to two decimal places)
So, the time taken to fill the tank when both pipes A and B are opened simultaneously is approximately 6.67 minutes, which is equivalent to 20 hours (since there are 60 minutes in an hour).
Therefore, the correct answer is option A) 20 hours.
Let's assume that the tank has a capacity of 1 unit.
Rate of filling by pipe A: 1/36 units per hour
Rate of filling by pipe B: 1/45 units per hour
Since the rates are given in units per hour, we can add them to get the combined rate:
Combined rate = 1/36 + 1/45
To add these fractions, we need to find a common denominator, which is the least common multiple (LCM) of 36 and 45. The LCM of 36 and 45 is 180.
So, let's rewrite the fractions with a common denominator of 180:
Combined rate = (180/36) + (180/45)
= 5 + 4
= 9 units per hour
Therefore, when both pipes A and B are opened simultaneously, they fill the tank at a rate of 9 units per hour.
Now, we can find the time taken to fill the tank by dividing the tank's capacity (1 unit) by the combined rate (9 units per hour):
Time taken = 1/9 hours
Since the question asks for the time taken in hours, we can convert the fraction to hours:
1/9 hours = (1/9) * 60 minutes
= 6.67 minutes (rounded to two decimal places)
So, the time taken to fill the tank when both pipes A and B are opened simultaneously is approximately 6.67 minutes, which is equivalent to 20 hours (since there are 60 minutes in an hour).
Therefore, the correct answer is option A) 20 hours.
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Two pipes A and B can fill a tank in 36 hours and 45 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?a)20 hoursb)30 hoursc)15 hoursd)25 hoursCorrect answer is option 'A'. Can you explain this answer?
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