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A tank can be filled by pipe X in 2 hours and pipe Y in 6 hours. At 10 a.m. pipe X was opened. At what time will the tank be filled if pipe Y is opened at 11 a.m.?
- a)12:45 am
- b)5:00 pm
- c)11:45 am
- d)11:50 am
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A tank can be filled by pipe X in 2 hours and pipe Y in 6 hours. At 10...
Suppose the capacity of tank = 6 units (LCM of 2 and 6)
⇒ Efficiency of X = 6/2 = 3 and Efficiency of Y = 6/6 = 1
Pipe X was opened at 10 am and pipe Y is opened at 11 am
Units of water filled by X in 1 hour (10 a.m. to 11 a.m.) = 3 units
⇒ Remaining units of water to be filled = 6 - 3 = 3 units
⇒ Time taken by (X + Y) to fill the remaining tank = ¾ hours = 45 minutes
∴ Tank will get filled at 11:45 a.m.
Most Upvoted Answer
A tank can be filled by pipe X in 2 hours and pipe Y in 6 hours. At 10...
Solution:
Let's assume that the capacity of the tank is 'C'.
Pipe X can fill the tank in 2 hours.
∴ In 1 hour, pipe X can fill 1/2 of the tank.
Pipe Y can fill the tank in 6 hours.
∴ In 1 hour, pipe Y can fill 1/6 of the tank.
Now, let's calculate the amount of water filled in the tank by pipe X in 1 hour, from 10 a.m. to 11 a.m. (when pipe Y is opened).
Time taken by pipe X from 10 a.m. to 11 a.m. = 1 hour
∴ Amount of water filled by pipe X in 1 hour = 1/2 of the tank
Now, both pipes X and Y are working together.
Combined rate of work = Rate of work of pipe X + Rate of work of pipe Y
= 1/2 + 1/6
= 2/3
∴ In 1 hour, both pipes working together can fill 2/3 of the tank.
Let's assume that the tank gets filled completely after t hours.
Amount of water filled by pipe X from 10 a.m. to t hours = (t-1) × 1/2 of the tank
Amount of water filled by pipe Y from 11 a.m. to t hours = (t-11) × 1/6 of the tank
As both pipes are working together, the sum of the above two amounts should be equal to the capacity of the tank 'C'.
∴ (t-1) × 1/2 + (t-11) × 1/6 = C
Simplifying the above equation, we get:
3t - 23 = 6C
∴ t = (6C + 23)/3
Now, we know that the tank gets filled completely. Hence, C is equal to 1.
∴ t = (6+23)/3
= 29/3 hours
= 9 hours and 40 minutes
Therefore, the tank will be filled at 11:00 a.m. + 9 hours and 40 minutes = 8:40 p.m.
But the question asks for the time at which pipe Y is opened.
Time taken from 11 a.m. to 8:40 p.m. = 9 hours and 40 minutes
∴ The tank will be filled at 11:00 a.m. + 9 hours and 40 minutes = 8:40 p.m.
Therefore, the correct answer is option (c) 11:45 a.m.
Let's assume that the capacity of the tank is 'C'.
Pipe X can fill the tank in 2 hours.
∴ In 1 hour, pipe X can fill 1/2 of the tank.
Pipe Y can fill the tank in 6 hours.
∴ In 1 hour, pipe Y can fill 1/6 of the tank.
Now, let's calculate the amount of water filled in the tank by pipe X in 1 hour, from 10 a.m. to 11 a.m. (when pipe Y is opened).
Time taken by pipe X from 10 a.m. to 11 a.m. = 1 hour
∴ Amount of water filled by pipe X in 1 hour = 1/2 of the tank
Now, both pipes X and Y are working together.
Combined rate of work = Rate of work of pipe X + Rate of work of pipe Y
= 1/2 + 1/6
= 2/3
∴ In 1 hour, both pipes working together can fill 2/3 of the tank.
Let's assume that the tank gets filled completely after t hours.
Amount of water filled by pipe X from 10 a.m. to t hours = (t-1) × 1/2 of the tank
Amount of water filled by pipe Y from 11 a.m. to t hours = (t-11) × 1/6 of the tank
As both pipes are working together, the sum of the above two amounts should be equal to the capacity of the tank 'C'.
∴ (t-1) × 1/2 + (t-11) × 1/6 = C
Simplifying the above equation, we get:
3t - 23 = 6C
∴ t = (6C + 23)/3
Now, we know that the tank gets filled completely. Hence, C is equal to 1.
∴ t = (6+23)/3
= 29/3 hours
= 9 hours and 40 minutes
Therefore, the tank will be filled at 11:00 a.m. + 9 hours and 40 minutes = 8:40 p.m.
But the question asks for the time at which pipe Y is opened.
Time taken from 11 a.m. to 8:40 p.m. = 9 hours and 40 minutes
∴ The tank will be filled at 11:00 a.m. + 9 hours and 40 minutes = 8:40 p.m.
Therefore, the correct answer is option (c) 11:45 a.m.
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A tank can be filled by pipe X in 2 hours and pipe Y in 6 hours. At 10 a.m. pipe X was opened. At what time will the tank be filled if pipe Y is opened at 11 a.m.?a)12:45 amb)5:00 pmc)11:45 amd)11:50 amCorrect answer is option 'C'. Can you explain this answer?
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A tank can be filled by pipe X in 2 hours and pipe Y in 6 hours. At 10 a.m. pipe X was opened. At what time will the tank be filled if pipe Y is opened at 11 a.m.?a)12:45 amb)5:00 pmc)11:45 amd)11:50 amCorrect answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about A tank can be filled by pipe X in 2 hours and pipe Y in 6 hours. At 10 a.m. pipe X was opened. At what time will the tank be filled if pipe Y is opened at 11 a.m.?a)12:45 amb)5:00 pmc)11:45 amd)11:50 amCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A tank can be filled by pipe X in 2 hours and pipe Y in 6 hours. At 10 a.m. pipe X was opened. At what time will the tank be filled if pipe Y is opened at 11 a.m.?a)12:45 amb)5:00 pmc)11:45 amd)11:50 amCorrect answer is option 'C'. Can you explain this answer?.
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