Question

A number consists of two digits whose sum is 10. If 18 is subtracted form the number, its digits are reversed. Find the number.

Answer 1

Let the number is xy = 10x + y   ...(1) 

∵ x is tens digit of the number and y is unit digit of the number

Given that sum of digits is 10.

∴ x + y = 10   ...(2)

Given that if 18 is subtract from the number then number is reversed 

It means becomes yx = 10y + x

Therefore, 10x + y – 18 = 10y + x

⇒ 9x – 9y = 18   ...(3)

Multiplying equation (2) by 9, we get

9x + 9y = 90   ...(4) 

Now adding equations (3) and (4), we get

9x – 9y + 9x + 9y = 18 + 90

⇒ 18x = 108

⇒ `x = 108/6`

⇒ x = 6

Now putting x = 6 in equation (2), we get 

6 + y = 10

⇒ y = 10 – 6

⇒ y = 4

Hence, the required number is

10x + y

= 10 × 6 + 4

= 60 + 4

= 64

By putting the values of x = 6 and y = 4 in equation (1)

Hence, the required number is 64.