Question

A 2-digit number is such that the product of its digits is 24. If 18 is subtracted from the number, the digits interchange their places. Find the number.

Answer 1

Let the ten's digit be x and the one's digit be y.

The number will be 10x + y

Given, a product of digits is 24

∴ xy = 24  

or, y = `24/x`  ...(i)

Given that when 18 is subtracted from the number, the digits interchange their places.

∴ 10x + y – 18 = 10y + x

or, 9x – 9y = 18  ...(ii)

Substituting y from equation (i) in equation (ii), we get

`9x - 9 (24/x)` = 18

or, `x - 24/x` = 2

or, x² – 24 – 2x = 0

or, x² – 2x – 24 = 0

or, x² – 6x + 4x – 24 = 0

or, x(x – 6) + 4(x – 6) = 0

or, (x – 6)(x + 4) = 0

or, x – 6 = 0 and x + 4 = 0

or, x = 6 and x = −4

Since, the digit cannot be negative, so, x = 6

Substituting x = 6 in equation (i), we get

y = `24/6` = 4

∴ The number = 10(6) + 4 = 60 + 4 = 64