Question

4. he sum of the digits of a two digit
number is 12. The number obtained by
interchanging the two digits exceeds the
given number by 18. Find the number. *
​

Answer 1

Answer:

the number is 57

When you interchange the digits 57 we get 75 the number exceeds by 18

Answer 2

Solution:

Let x and y be the 2 digits.

Required Number:

T  |  O

x  |   y

So, the value of the required number would be (10x + y)

Similarly, on reversing the digits, the number obtained would be (10y + x)

According to the Question:

x + y = 12          ----- [Equation 1]

⇒ y = 12 - x

(10y + x) = 18 + (10x + y)

⇒ 10y + x = 18 + 10x + y

⇒ 10y - y = 18 + 10x - x

⇒ 9y = 18 + 9x

⇒ 9y - 9x = 18

⇒ 9 (y - x) = 18

⇒ y - x = 2        ----- [Equation 2]

Add Equation 1 and Equation 2

               x + y = 12

     {+}     - x + y = 2  

                      2y = 14

⇒ y = 7

Substitute the value of y in Equation 1 to find the value of x.

x + y = 12

⇒ x + 7 = 12

⇒ x = 5

∴ The required number is (5 × 10) + 7 = 57