A two digit number is such that the product of the digits is 24. when 18 is subtracted to the number

The product of the digits of a two digit positive number is 24. If 18 is added to the number then the digits of the number are interchanged. Find the number.

Asked by Topperlearning User | 26 Jul, 2017, 12:56: PM

Let the digit at ten's place = x

Then, digit at one's place =

Original number = 10x +

On interchanging the digits, new number =

According to the question,

10x +

10x2 + 24 + 18x = 240 + x2

9x2 + 18x - 216 = 0

x2 + 2x - 24 = 0

(x + 6) (x - 4) = 0

x = -6 or 4

But x can't be negative, so, x = 4

Digit at ten's place = x = 4 and digit at one's place =

= 6

Thus, the original number is 46.

Answered by | 26 Jul, 2017, 02:56: PM