Question

Sum of the digits of a 2 digit number is 10. The number obtained by interchanging the digits exceeds the given number by 36 .find the number​

Answer 1

Given :-

The Sum of the digits of a 2 digit number is 10.

The number obtained by interchanging the digits exceeds the given number by 36

To Find :-

Number

Solution :-

Let, the number at tens place be x. Unit place be y

x + y = 10 (1)

Original number = 10x + y

Reversed number = 10y + x

10x + y + 36 = 10y + x

10x - x + 10y - y = 0 - 36

9x - 9y = -36

(9x - 9y)/9 = (-36)/9

x - y = -4 (ii)

On adding

x + y + x - y = 10 + (-4)

(x + x) = 10 - 4

2x = 6

x = 6/2

x = 3

Using 2

x - y = -4

3 - y = -4

-y = -4 - 3

-y = -7

y = 7

Original number = 10x + y

Original number = 10(3) + 7

Original number = 30 + 7

Original number = 37

Answer 2

Answer:

Let the tens place digit be a

And Unit place digit be b

a + b = 10 ---(1)

10a + b + 36 = 10b + a

=> 9a - 9b = - 36

=> a - b = - 4 ----(2)

Adding equation 1 and 2, we get

2a = 6

a = 3

Now, On putting the value of a in equation 1, we get

b = 7

Required number = 37