Question

The sum of digits of two - digit number is 15. The number is decreased by 27, if the digits are reversed, Find the number

Answer 1

Let the digits be x and y... and so, the original number be 10x + y ( since x in tenth place and y in unit place)

so, given : sum of the digits = x + y = 15 ---------> (A)
                  
reversing the digits means y in tenth place and x in unit place.. so, the reversed number be 10y + x
         
   given: if the original number is reversed it is decreased by 27 
 
          so, 10y + x = (10x + y) - 27 
           simplifying :   x - y = 3       ------------> (B)

solving 2 eqns (A) & (B) ,
 we get x = 9 and y = 6

so the original number is 10x + y = 10(9) + 6 = 96
   & the reversed number is 10y + x = 10(6) + 9 = 69
    & the reversed number 69 is got when the original number 96 is decreased by 27 (69 = 96 - 27)

Ans: the original number is 96

Answer 2

Answer:

Let the digit at the unit place be x.

Then, the digit in the tens place =(15−x)

∴ Original number =10×(15−x)+x=150−9x

On reversing the digits, we have x at the tens place and (15−x) at the unit place.

∴ New number =10x+(15−x)=(9x+15)

According to the given condition,

(Original number) − (New number) =27

⇒(150−9x)−(9x+15)=27

⇒150−9x−9x−15=27

⇒135−18x=27

⇒18x=135−27

⇒x=(

18

108

)=6

∴ In the original number, we have units digit =6 and tens digit =(15−6)=9

Hence, the original number is 96.