QUESTION

CSAT

Medium

Maths

Prelims 2018

A number consists of three digits of which the middle one is zero and their sum is 4. If ‘he number formed by interchanging the first and last digits is greater than the number itself by 198, then the difference between the first and last digits is

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Explanation

Let the hundreds digit be xx, the tens digit be 0, and the ones digit be yy. The original number is: 100x+10y100x + 10y

The number formed by interchanging the first and last digits is: 100y+10x100y + 10x

The given information is: 100y+10x(100x+10y)=198100y + 10x - (100x + 10y) = 198

Simplifying: 90(yx)=19890(y - x) = 198

Dividing both sides by 90: yx=2y - x = 2

Also, it is given that the sum of the digits is 4: x+y=4x + y = 4

Now, solving these two equations: x+y=4x + y = 4 yx=2y - x = 2 Adding both equations: (x+y)+(yx)=4+2(x + y) + (y - x) = 4 + 2 2y=6y=32y = 6 \rightarrow y = 3

Substituting y=3y = 3 into x+y=4x + y = 4: x+3=4x=1x + 3 = 4 \rightarrow x = 1

Therefore, the difference between the first and last digits is: yx=31=2y - x = 3 - 1 = 2

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