Question

The sum of the digits of a two-digit

number is 7. When the digits are reversed, the number is

increased by 27. Find the number.

Short answer

For the given problem the digits are 2 and 5, in ten’s and one’s digit respectively. Hence the original number is 25.

Step-by-step solution

Step 1. Given information.

$x+y=7$ ……..(1)

x = ten’s digit of the original number

y = one’s digit of the original number

Step 2. Write down the concept.

Number before and after reversing is 10x + y and 10y + x respectively.

Now, by the given information that the value is increased, on reversing the digits, by 27 we have,

(10y + x) – (10x + y) = 27

-9x + 9y = 27

-x + y = 3 ……..(2)

Step 3. Determining the angle

By elimination method one can solve two equations by adding (1) and (2) to get.

2y = 10

y = 5

substituting in (1) we get,

x + 5 =7

x = 2

Thus, the original number is 25.