Question

Q.1. A two-digit number is such that the sum of the digits is 11. When the
number with the same digits is reversed is subtracted from this number,
the difference is 9. What is the number?*​

Answer 1

=> Let’s call one of the digits X and the other Y, and then we know the following:

X + Y = 11

(10X + Y) - (10Y + X) = 9

So let’s simplify the second equation

10X - X + Y - 10Y = 9

9X - 9Y = 9

Now we have the two equations

X + Y = 11

9X - 9Y = 9

and we can solve the system of equations.

First, let’s multiply the first equation by 9 and then add them together:

9X + 9Y = 99

9X - 9Y = 9

or

18X = 108 (as the Y’s cancel out above)

giving X = 6

Inserting it into the first of the equations gives quickly Y = 5 and thus we have the two numbers, 65 and 56 that match the criteria from the question.

However, as the question states, the number with it’s digits reversed subtracted from the number gives 9 as the result, so only the larger of those is suitable to answer the question.

Answer 2

Step-by-step explanation:

x+ y = 11.................1

(1Ox+ y) - ( 1O y - x )=9

9x-9y=9

x-y=1.........2

adding eq.1 and2

2x = 12

x = 6

put x = 6 in equation 1

6+ y = 11

y = 11- 6 = 5

(x,y)= (6,5)

65 is number

mark as brainliest and give thanks please i need