Question

the sum of two digits of a two digit number is 15 . The number obtained by reversing the order of digits of a given number exceeds the given number by 9 . Find the given number , solve it by elimination method only ....​

Answer 1

Given :-

Sum of digits of a two-digit numbers is 15.The number obtained by interchanging its digits exceeds the given number by 9.

To Find :-

The Original Number

Solution :-

Let the tens digit number be x

And the units digits number be y

Original number = (10x + y)  

According to the Question

1st Equation

x + y = 15 ……..(i)  

2nd Equation

Number obtained on reversing its digits = (10y + x)  

⇒ (10y + x) = (10x + y) + 9  

⇒ 10y + x – 10x – y = 9  

⇒ 9y – 9x = 9  

⇒ y – x = 1 …….(ii)  

On adding (i) and (ii)

⇒ 2y = 16  

⇒ y = 8  

Putting all the values in Eq (i)

⇒ x + y = 15

⇒ x + 8 = 15  

⇒ x = (15 – 8)

⇒ x = 7  

Number = (10x + y)

= 10 × 7 + 8

= 70 + 8

= 78  

Hence, the original number is 78

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