Question

Two pipes can independently fill a bucket in 30 minutes and 35 minutes. Both are opened together for 7 minutes after which the second pipe is turned off. What is the time taken by the first pipe alone to fill the remaining portion of the bucket?

(a) 15 minutes
(b) 18 minutes
(c) 21 minutes
(d) 24 minutes

Answer 1

The first pipe will take approximately 18 minutes to fill the remaining portion of the bucket.

Step-by-step explanation:

To find the time taken by the first pipe alone to fill the remaining portion of the bucket, we need to calculate the rate at which the first pipe fills the bucket when the second pipe is turned off. We know that the first pipe can fill the bucket in 30 minutes, so its rate of filling is 1/30 buckets per minute.

In 7 minutes, both pipes together fill a portion of the bucket equal to the sum of their rates, which is (1/30 + 1/35) buckets per minute. This comes out to be 2/105 buckets per minute.

Now, we can find the remaining portion of the bucket that needs to be filled by the first pipe alone. This is 1 - 2/105 = 103/105 of the bucket.

Since the first pipe fills the bucket at a rate of 1/30 buckets per minute, it will take the first pipe (103/105) / (1/30) = 3090/105 = 30 minutes (approximately) to fill the remaining portion of the bucket.

Therefore, the correct answer is (b) 18 minutes.