Question

A two digit number is obtained by either multiplying the sum of the digits by 8 and adding 1,or by multiplying the difference of the digits by 13 and adding 2. Find the number? How many such numbers are there?(Ans : 41 case 2 When the difference is y-x , y = -19/137, which is a fraction . so invalid)

Answer 1

Let us assume, x and y are the two digits of the two-digit number

Therefore, the two-digit number = 10x + y

Given:

10x + y = 8 * (x + y) + 1

10x + y = 8x + 8y + 1

2x – 7y = 1 ----------------1

Also given:

10x + y = 13 (x – y) + 2

10x + y = 13x – 13y + 2

14y – 3x = 2

Or – 3x + 14y = 2-----------2

Multiply equation 1 by 2

4x – 14y = 2 ------------3

Add equation 2 and 3

x = 4

Substitute the value of x in equation 1

2 * 4 – 7y = 1

8 – 7y = 1

7y = 7

y = 1

Therefore, the two-digit number = 10x + y = 10 * 4 + 1 = 41

There are only one number and that is 41.