Question

A two digit number is obtained by either multiplying the sum of digits by 8 and then subtractng 5 or by multiplying the difference of digits by 16 and adding 3. Find the number.

Answer 1

Let us assume x and y are the two digits of the 2 digit-number

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

Given:

10x + y  = 8 (x + y) – 5

10x + y = 8x + 8y – 5

7y – 2x = 5 ---------------1

Also given:

10x + y = 16 (x – y) + 3

10x + y = 16x – 16y + 3

17y – 6x = 3 ------------ 2

Adding equation 1 and equation 2

24y – 8x = 8

3y – x = 1

x = 3y – 1 ---------------3

Substitute the value of x in equation 1

7y – 2 (3y - 1) = 5

7y – 6y  +  2 = 5

y = 3

Therefore, x = 3y – 1 = 3*3 – 1 = 8

Therefore, the two-digit number = 10x + y = (10 * 8) + 3 = 83