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
• B. 12
• C. 13
• D. 14

Answer 1

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. $1\times 1+2\times 2+........N\times n=1002.$

N=13.93

i.e. when the ${14}^{th}$ tap is open the tank gets filled.