Question

if the number obtained by interchanging the digits of a two digit number is 36 more than the original number and the sum of the digits is 6 then what is the original number.​

Answer 1

Answer:

15

Step-by-step explanation:

Let the required number is ab which can also be written as 10a + b.

  As given, sum of digit = 6 = a + b

              ⇒ a = 6 - b

According to question: On interchanging the digits, new number is 36 more than original. New number is ba or 10b + a.

⇒ 10a + b + 36 = 10b + a

⇒ 9a - 9b = - 36

⇒ a - b = - 4

⇒ 6 - b - b = - 4

⇒ 6 + 4 = 2b

⇒ 5 = b

          Hence, a = 6 - 5 = 1

Therefore the required number is ab = 15

Answer 2

$\Large{\underline{\underline{\bf{\blue{Given}}}}}$

If the number obtained by interchanging the digits of a two digit number is 36 more than the original number and the sum of the digits is 6

$\Large{\underline{\underline{\bf{\blue{To\:find}}}}}$

what is the original number.

$\Large{\underline{\underline{\bf{\blue{Solution}}}}}$

★ Let the tens digit be x unit digit be y

• Original number = 10x + y

**According to the given condition**

★ Sum of the digit is 6

• x + y = 6

★ The number obtained by interchanging the digits of a two digit number is 36 more than the original number

• Interchanged number = 10y + x

➨ 10y + x = 10x + y + 36

➨ 10y - y + x - 10x = 36

➨ 9y - 9x = 36

➨ 9(y - x) = 36

➨ -x + y = 4

Add both the equations

➨ (x + y) + (-x + y) = 6+4

➨ x + y - x + y = 10

➨ 2y = 10

➨ y = 5

Put the value of y in eqⁿ (ii)

➨ - x + y = 4

➨ -x + 5 = 4

➨ x = 5 - 4 = 1

Hence,

Original number = 10x + y = 15