Question

a number consists of 2 digits whose sum is 11. if the digits are interchanged the value of the number decreases by 45. find the numbers.

Answer 1

Answer:

Step-by-step explanation:

Let’s Suppose first digit is x and second digit is y

so, the two digit number is: 10x + y

sum of digits: x + y = 11

if digits are reversed then the new number: 10y + x

new number is 9 less than original number: (10x + y) - (10y + x) = 9

So, ultimately we got two equations to solve:

1. x + y = 11

2. (10x + y) - (10y + x) = 9

Now, let’s solve equation 2,

(10x + y) - (10y + x) = 9

=> 10x + y - 10y - x = 9

=> 9x - 9y = 9

=> 9 ( x - y ) = 9

=> x - y = 9/9

=> x - y = 1

=> x = 1 + y

Let’s put this value of x in equation (1),

x + y = 11

=> 1 + y + y = 11

=> 2y + 1 = 11

=> 2y = 11 - 1

=> y = 10/2

=> y = 5

Now, let’s put y = 5 in equation (1),

x + y = 11

=> x + 5 = 11

=> x = 11 - 5

=> x = 6

So, the original number is: 10x + y = 10*6 + 5 = 65

Ans: 65

Answer 2

Answer:answer is 83

Step-by-step explanation:

Refer to the pic