Question

The product of the digits of a two digit number is 24. If its unit’s digit exceeds twice its ten’s digit by 2; find the number.

Answer 1

Let the ten’s and unit’s digit of the required number be x and y respectively.

From the given information,

x × y = 24

y = `24/x`  ...(1)

Also, y = 2x + 2  

`24/x = 2x + 2`   ...[Using (1)]

24 = 2x² + 2x

2x² + 2x – 24 = 0

x² + x – 12 = 0

(x + 4)(x – 3) = 0

x = – 4, 3

The digit of a number cannot be negative, so x = 3

∴ y = `24/3` = 8

Thus, the required number is 38.