Question

'N' is a three digit number. It exceeds the three digit number formed by reversing the digits by 792. Find its hundred's digit.

Answer 1

The answer is 396 as you have divide 792 by 2.

Answer 2

Answer:

Hundred's Digit: 9

Step-by-step explanation:

Let the digits of the three-digit number be x, y and z respectively.

x - Hundred's digit (to be found)

y - Tens digit

z - Unit(Ones) digit

Case 1:

100x + 10y + z = N (given) --------- (1)

Case 2:

100z + 10y + x + 792 = N (given - reversing the digits) ---------- (2)

Equating (1) and (2),

100x + 10y + z = 100z + 10y + x + 792

100x + 10y + z - 100z - 10y - x = 792

99x - 99z = 792 ----------- (3)

divide (3) by 99,

x - z = 8

x = 8 + z ---------- (4)

If z = 0,

x = 8 + 0

x = 8

If z = 1,

x = 8 + 1

x = 9

If z = 0, when reversing it becomes a two-digit number(0y8) but the question clearly states if reversed it is a three digit number.

So, z = 0 and x = 8 is not possible.

Therefore the only answer is z = 1 and x = 9

So, the hundred's digit is 9.