Question

Sum of the digits of a two-digit number is 9. When we interchange the digits, it is
found that the resulting new number is greater than the original number by 27. What
is the two-digit number?​

Answer 1

Step-by-step explanation:

Let the two digit number will be 36

If we add two digits 3+6=9

If we reverse the number we get 63

63-36=27

The reversed number is greater by 27 therefore the two digit number is 36.

Answer 2

Step-by-step explanation:

Given:

• Sum of two digits of a two digit number is 9
• After interchanging its digits the resulting number is greater than original by 27

To Find:

• What is the two digit number

Solution: Let the unit digit of number be y and tens digit be x

∴ Number will be = 10x + y

• After reversing number will be = 10y + x

• x + y = 9 ( Sum of numbers is 9) ................eq(1)

A/q

$\small\implies{\sf }$ 10y + x = 10x + y + 27.................eq(2)

$\small\implies{\sf }$ 10y – y = 10x – x + 27

$\small\implies{\sf }$ 9y = 9x +27

$\small\implies{\sf }$ 9y – 9x = 27

$\small\implies{\sf }$ 9(y – x) = 27

$\small\implies{\sf }$ y – x = 27/9

$\small\implies{\sf }$ y – x = 3

★ By solving equations 1 and 2 we will get

• x = 3 and y = 6

Therefore, Original number is 36

After reversing it will 63

And Difference between these two number is → 63–36 = 27