Question

A number has two digits whose sum is 9. If 27 is added to the number, its digits gets
interchanged. Find the number.​

Answer 1

Answer:

36

Step-by-step explanation:

Let digit in 1s place of original number = x

Let digit in 10s place of original number = y

Original number is 10y + x

Sum of digits is 9 => x + y = 9 .......(i)

Number obtained on interchanging the digits will be 10x + y

Given: Original number + 27 = Interchanged number

=> 10y + x + 27 = 10x + y

=> 9x - 9y = 27

=> x - y = 3 ...........(ii)

Adding (i) and (ii), we get:

2x = 12

=> x = 6

Using (i), we get:

y = 9 - x = 9 - 6 = 3

=> y = 3

The original number = 10y + x = 10*3 + 6 = 36

Verification:

Original number = 36

Original number + 27 = 36 + 27 = 63 = Interchanged number (verified)