Question

The sum of the digits of a two digits number is 15.The number is decreased by 27, if the digits are

reversed. Find the number.​

Answer 1

Answer:

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

Step-by-step explanation:

Answer 2

Answer :

Assume that the digit at one's place be as m and digit at ten's place be as n.

• Original Number = 10m + n
• Reversed Number = 10n + m

• We are given that, the sum of the digits of a two digits number is 15; mathematically :

⇒m + n = 15

⇒m = 15 - n ...(eqⁿ i)

• We are also provided that,If the digits are reversed, the number is reduced by 27; mathematically :

⇒10m + n - 27 = 10n + m

⇒10m + n - (10n - m) = 27

⇒9m - 9n = 27

⇒9(m - n) = 27

⇒m - n = 27 ÷ 9

⇒m - n = 3

⇒15 - n - n = 3 [From eqⁿ (i)]

⇒15 - 2n = 3

⇒-2n = 3 - 15

⇒-2n = -12

⇒2n = 12

⇒n = 6

Substituting the value of n = 6 in eqⁿ (i) :

⇒m = 15 - n

⇒m = 15 - 6

⇒m = 9

◖Original Number :

⇒Original number = 10m + n

⇒Original number = 10(9) + 6

⇒Original number = 90 + 6

⇒Original number = 96

• Hence,the required number is 96.