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Question

Taps to a tank are switched on in the following manner. Tap 1 for the first hour. Tap 2 for the next two hrs and so on.The number indicated on each tap (1 for Tap number 1, 2 for tap number 2...) indicates its flow rate in litre/hr. These taps are filling a tank whose capacity is more than 1000 litre. Moreover the capacity cannot be expressed as a difference of squares of two numbers. Find the tap no that fills the tank assuming that the tank's capacity is minimum.

A

11

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B

12

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C

13

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D

14

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Solution

The correct option is D 14 The smallest number possible is 1002 (this is a 4k+2 number, it cannot be expressed as difference of squares) . Therefore our equation becomes. 1×1+2×2+........N×n=1002. N=13.93 i.e. when the 14th tap is open the tank gets filled.

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