11. The 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.?

Question

Answer

Problem Statement: The 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.

Solution:

Let the tens digit of the given number be x and the units digit be y.

According to the problem statement,

x + y = 12 (Equation 1)

The number obtained by interchanging the two digits is given by 10y + x. This number exceeds the given number (10x + y) by 18. Therefore,

10y + x = 10x + y + 18

Simplifying this equation, we get

9y - 9x = 18

y - x = 2 (Equation 2)

Now we need to solve Equations 1 and 2 simultaneously to find the values of x and y.

Adding Equations 1 and 2, we get

2y = 14

y = 7

Substituting this value of y in Equation 1, we get

x + 7 = 12

x = 5

Therefore, the required two digit number is 57.

Answer: The required number is 57.

Answer

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