Question

The sum of the digits of a two-digit number is 9.
When we interchange the digits, it is found that the resulting new number is greater than the original number by 45.
What is the two-digit number?

Answer 1

Answer:

x=2 and y=7

Step-by-step explanation:  

  x + y = 9 .....eq 1

AND

  10y+x-(10x+y) = 45

=>y-x = 5.....eq 2

Solving simultaneously eq 1 and 2 you will get x=2 and y= 7  

Answer 2

$\huge\blue{Answer}$

$let \: the \: two \: digit \: number \: be \: 10a \: +\: b$

so,10a+b=9[equation 1]

number obtained after reversing the digits

= 10b+a.

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difference of two numbers = 45.

. i.e (10a+b)-(10b+a) = 45

we get,

10a+b - 10b-a=45

9a-9b = 45

9(a - b)=45

a - b=5

a - b = 45[equation 2]

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Putting the two equations we get:

a + b = 9

a - b = 5 {by adding)

______

2a = 14

a = 7

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putting the value in the equation 1 ,we get:

7 + b = 9

b = 2.

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so ,the required number is

10(7)+2

72.

$<marquee>Hope it helps you</marquee>$