Question

The sum of digits of a two number is 15. The number obtained by reversing the order of digits of the given number exceeds the given number by 9. Find the given number.

Answer 1

Given : The sum of digits of a two number is 15. The number obtained by reversing the order of digits of the given number exceeds the given number by 9.  

Solution:

Let the digit in the unit's place be x and the digit at the tens place be y.

Number = 10y + x

The number obtained by reversing the order of the digits is = 10x + y

ATQ :

Condition : 1

x + y = 15 ………….(1)

Condition : 2

10x + y = 10y + x + 9

10x + y – 10y – x = 9

9x – 9y = 9

9(x – y) = 9

x – y = 1 …………….(2)

On adding equations (1) and (2) :

x + y = 15

x - y = 1

-----------------

2x = 16

x =  16/2

x = 8

On putting x = 8 in eq (1)  we obtain :  

x + y = 15

8 + y = 15

y = 15 - 8

y = 7

Now, Number = 10y + x = 10 × 7 + 8 = 70 + 8 = 78

Hence, the number is 78.

Hope this answer will help you…

 

Some more questions from this chapter :  

The sum of digits of a two digit number is 13. If the number is subtracted from the one obtained by interchanging the digits, the result is 45. What is the number?

https://brainly.in/question/17174034

Answer 2

Solution :

Let the ten's and units digit of a number be ' x ' and ' y '

Here ,,, xy = 10x + y

According to the question ,,,,,,

==> x + y = 15

x = 15 - y -------------- eq (1)

==> 10y + x = 9 + 10x + y

10y - y = 9 + 10x - x

9y = 9 + 9x

Now, divide both side by 9 ,,, we get ......,,

y = x + 1

y = ( 15 - y ) + 1 ------------------ { from eq 1 }

y = 14 - y

y + y = 14

2y = 14

y = 7

Put y = 7 in eq ( 1 ) we get,,,

==> x = 15 - y

x = 15 - 7

x = 8

Therefore ,,,, the required number is 87 .....

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