Question

A number consists of two digits. The sum of its digits is 16. If 28 is subtracted from the number, the digits interchange their place. Find the number. |.Give the answer only ​

Answer 1

• The number is 97

Explanation:

Note: The difference should read 18 not 28, it must be a typo. In general such difference must be a multiple of 9.

Let the digits are x and y.

If the first digit is x and the second digit is y, then the number is 10x + y.

According to the question we have:

• x + y = 16
• 10x + y - 18 = 10y + x ⇒ 9x - 9y = 18 ⇒ x - y = 2

Add up the equations:

• x + y + x - y = 16 + 2
• 2x = 18
• x = 9

Find y:

• 9 + y = 16
• y = 7

The number is 97.