Latest MBA Aptitude Question SOLUTION: There are t taps numbered 1,2 and so on till t, each of which can fill a cistern. the rate of filling of the nth ta is such that it is equal to twice that of all the taps from 1 to

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(#M40015904) MBA Logical Reasoning question time speed and distance, work, alligations & mixtures Keep an EYE

There are t taps numbered 1,2 and so on till t, each of which can fill a cistern. the rate of filling of the nth ta is such that it is equal to twice that of all the taps from 1 to (n-1) put together. If the 18th tap can fill the cistern in 2 minutes, then find the time in which the 15th tap alone can fill the empty cistern.

1) 27
2) 34
3) 54
4) 72

Asked In MBA (11 years ago)

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Read Solution (1) :

Piyush Kumar  (9 years ago)

Let 1st tap can fill the cistern in T mins.
2nd tap: T/2 mins
3rd tap: half the time taken by 1st and 2nd tap combined. : (T/3)/2 = T/6
4th tap: half the time taken by 1st, 2nd and 3r combined. : (T/9)/2 = T/18

Similarly,
5th tap : (T/27)/2 = T/54
..
nth tap: T/(3^(n-2)*2)

Now we have,
18th tap: 2 mins
=> T/(3^(18-2)*2) = 2
Hence, T = 2^2 * 3^16

Now, for 15th tap,
Time taken = T/(3^(n-2)*2) = (2^2 * 3^16) / (3^(15-2)*2) = 2 * 3^3 = 54
Hence time taken by 15th tap is 54 minutes.

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