Question

3. The sum of digits of a two digit number is 7. The number obtained, on reversing the order of digits is
greater than original number by 9. ​

Answer 1

Let the 2 digit number be xy

Ten's digit = x

Unit's digit = y

Given:

x + y = 7

To Find:

2 digit number xy

Method:

x + y = 7 or y + x = 7

When the digits are reversed, number becomes 9 more than original number.

Since x is in Ten's place, It's value becomes 10x

So, The original number now is: 10x + y

When we reverse the digits of the original number, it becomes: 10y + x

So, The Equation becomes,

10y + x = (10x + y) + 9

⇒ 10y + x = 10x + y + 9

⇒ 10y - y = 10x - x + 9

⇒ 9y = 9x + 9

⇒ 9y - 9x = 9 or y - x = 1 ...... (Taking 9 out as common on both sides)

Now, we have -

y + x = 7

y - x = 1

Adding the above equations,

⇒ 2y = 8 or y = 4

Substituting in any one equation;

y - x = 1

⇒ 4 - x = 1

⇒ 4 - 1 = x or x = 3

The required number is 10x + y = 10(3) + 4 = 34

Verification:

3 + 4 = 7

43 - 34 = 9