Three taps A, B and C can fill a cistern in 12, 15 and 18 min respectively. They are all turned on but after 4.5 minutes A and C are turned off. How many more minutes will B take to fill the cistern?Marks : 2Negative Marks : 0Answer here1.125 min4.5 min5.625 minNone of these
Question
Three taps A, B and C can fill a cistern in 12, 15 and 18 min respectively. They are all turned on but after 4.5 minutes A and C are turned off. How many more minutes will B take to fill the cistern?Marks : 2Negative Marks : 0Answer here1.125 min4.5 min5.625 minNone of these
Solution
First, let's find out how much of the cistern each tap can fill in one minute.
Tap A can fill 1/12 of the cistern in one minute. Tap B can fill 1/15 of the cistern in one minute. Tap C can fill 1/18 of the cistern in one minute.
When all taps are turned on together, they can fill (1/12 + 1/15 + 1/18) = 1/5 of the cistern in one minute.
In 4.5 minutes, they can fill 4.5 * (1/5) = 0.9 or 90% of the cistern.
After 4.5 minutes, taps A and C are turned off, leaving only tap B running. Tap B can fill 1/15 of the cistern in one minute.
The remaining 10% of the cistern will be filled by tap B alone. So, the time taken by tap B to fill the remaining part of the cistern is 10% divided by (1/15) = 1.5 minutes.
So, tap B will take 1.5 more minutes to fill the cistern after taps A and C are turned off.
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