Question

The sum of the digits of a two-digit number is 15. When the number obtained by reversing the digits is subtracted from the original number, we get the difference of 9. Find the original number?

1. 87
2. 96
3. 69
4. 78

Answer 1

Correct Answer - Option 1 : 87

Given:

The sum of digits of a two-digit number is given as 15.

Calculation:

Let the two-digit number be XY and the reverse number is YX

A two digit number XY can be written as = 10X + Y     (Like 52 = 50 + 2)

As the sum of the digits of the number XY is 15

⇒ X + Y = 15      ____(1)

Also the reverse number is YX = 10Y + X

Now subtract the original and the reverse number

⇒ 10Y + X – (10X + Y) = 9Y – 9X

⇒ 9(X – Y) = 9 (Given)

⇒ X – Y = 1      ____(2)

From equation (1) & (2) we get

⇒ X + Y = 15

⇒ X – Y = 1

2X = 16, X = 8 (put this in any of the above equation)

We get Y = 7

∴ The original number is XY = 87

Original number is 87

According to the condition,

sum of digit = 8 + 7 = 15

and reverse the digit 78, Difference both the number 

⇒ 87 - 78 = 9

If we take 78 as original number 

The First condition is satisfied, but the reverse number is subtracted then gets a negative number. 

⇒ 78 - 87 = - 9 

That's why 78 is not the correct answer.