1.

A three-digit number is such that when its reverse is subtracted from it, the result is 396. Also, the tens digit is equal to the average of its hundreds and units digits. How many possible values are there for the number?1. 72. 63. 54. 4

Answer» Correct Answer - Option 2 : 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.


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