Question

The sum of the digits of a two – digit number is 14. If the digits are reversed, the number increases by 36 . Find the number.

Answer 1

Answer:

59

Step-by-step explanation:

Explanation:

Let the unit's digit be  

x

as sum of digits is  

14

, ten's digit is  

14 − x ,

then the number is  

10 × ( 14 − x ) + x

i.e.  

140 − 10 x + x

or  

140 − 9 x

Reversing the digits number, unit digit becomes  

14 − x

and tens digit becomes  

x , hence number is  

10 x + 14 − x = 9 x + 14 .

As adding  

36 to  140 − 9 x  makes it  9 x + 14 , we have  

140 − 9 x + 36 = 9 x + 14  

 

176 − 14= 9 x + 9 x  

18x = 162  X = 9

and hence, unit''s digit is  

9

and tens digit is  

5

and number is  

59

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