How many three digit numbers are possible such that the difference between the original number and t...........

Quantitative Aptitude( Paper-I ) Number System

How many three-digit numbers are possible such that the difference between the original number and the number obtained by reversing the digits is 396 ? (no digit is repeated)

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CAPF 2023 Paper-1

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Explanation:

Correct answer is option 4: 6

Let's assume a, b, c be the hundreds, tens and units digits of the desired number.
So, the desired number 'abc' = 100a + 10b + c
After reversing it, it becomes 'cba' = 100c + 10b + a
Now, 'abc' - 'cba' = (100a + 10b+c) - (100c + 10b + a)
⇒396 = 99(a- c)
⇒(a - c) = 396/99 = 4
Thus, possible combination of (a, c) = ((9, 5), (8, 4), (7, 3), (6, 2), (5, 1), (4, 0)}
For every combination of (a, c) only one value of b is possible.
So in all, there are 6 such numbers possible.