Two pipes can separately fill a tank in 20 hours and 30 hours respectively. Both the pipes are opened to fill the tank but when the tank is 3/4thfull, a leak develops in, through which one-fourth of water supplied by both the pipes goes out. What is the total time taken to fill the tank?a)18 hoursb)14 hoursc)15 hoursd)13 hoursCorrect answer is option 'D'. Can you explain this answer?

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Two pipes can separately fill a tank in 20 hours and 30 hours respectively. Both the pipes are opened to fill the tank but when the tank is 3/4^th full, a leak develops in, through which one-fourth of water supplied by both the pipes goes out. What is the total time taken to fill the tank?

a)
18 hours
b)
14 hours
c)
15 hours
d)
13 hours

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

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Two pipes can separately fill a tank in 20 hours and 30 hours respecti...

Answer: Option D

Explanation :Time to completely fill the tank by the two pipe:

1/20 + 1/30= 1/n

⇒ n = 12 hours

So, 3/4^th of the tank will be filled in 3/4 × 12 = 9 hours.

Remaining time = 12 – 9 = 3 hours.

But, for the remaining 1/4^th of the tank, the combined efficiency drops to 3/4^th (1/4^th is getting leaked),

∴ Time required will be come 4/3 times, i.e. 4/3 × 3 = 4 hours.

Hence, total time taken to fill the tank = 9 + 4 = 13 hours.

Hence, option (d).

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Two pipes can separately fill a tank in 20 hours and 30 hours respecti...

Understanding the problem:
- Pipe 1 can fill the tank in 20 hours.
- Pipe 2 can fill the tank in 30 hours.
- When the tank is 3/4th full, a leak develops and one-fourth of the water supplied by both pipes goes out.

Solution:
1. Let's calculate the filling rate of each pipe:
- Pipe 1 can fill 1/20 of the tank in 1 hour.
- Pipe 2 can fill 1/30 of the tank in 1 hour.
2. When the tank is 3/4th full, the total amount of water in the tank is 3/4 of the tank's capacity.
3. At this point, the leak starts and one-fourth of the water supplied by both pipes goes out. This means only 3/4 of the water supplied by both pipes remains in the tank.
4. Let the total time taken to fill the tank be x hours. In x hours, the combined filling rate of both pipes is 1/x of the tank's capacity.
5. The effective filling rate after the leak starts is (3/4) * (1/20 + 1/30) = (3/4) * (1/20 + 1/30) = (3/4) * (1/12) = 1/16 of the tank's capacity.
6. Equating the effective filling rate to the combined filling rate:
1/x = 1/16
x = 16 hours
Therefore, the total time taken to fill the tank is 16 hours, which corresponds to option 'D'.

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Two pipes can separately fill a tank in 20 hours and 30 hours respectively. Both the pipes are opened to fill the tank but when the tank is 3/4thfull, a leak develops in, through which one-fourth of water supplied by both the pipes goes out. What is the total time taken to fill the tank?a)18 hoursb)14 hoursc)15 hoursd)13 hoursCorrect answer is option 'D'. Can you explain this answer?

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