Math, asked by aniketkumar1111, 7 months ago

The sum of the digits of a 2-digit number is 11. If we add 45 to the number, the new number obtained is a number formed by the interchange of the digits. What is the number?​

Answers

Answered by MinalBuchke
2

Answer:

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Step-by-step explanation:

Let the first digit of number be x and second digit of number be y.

So the number will look like xy Or 10*x + y

x + y = 11 and,

10*x + y + 45 = 10*y + x

Putting, y = 11 - x in above equation

10*x + (11 - x) + 45 = 10*(11 - x) + x

10x + 11 - x + 45 = 110 - 10x + x

18x = 54

x = 3

And as y = 11 - x, so y = 8

Therefore the number is 38.

Thank you

Answered by rinsybeo
1

Step-by-step explanation:

Let the ten's place be = x

Let the unit place be = y

original number = 10x + y

reversing number = 10y + x

Case = 1.

The sum of digit of a two digit number is = 11

=> x + y = 11 ...... (1)

Case = 2.

If 45 is added to the number the new number

obtained is a number formed by the

interchanging of its digit.

=> 10x + y + 45 = 10y + x

=> 9x - 9y = -45

=> x - y = -5 ..... (2)

From equation (1) and (2) we get,

=> 2x = 6

=> x = 3

put the value of x = 3 in equation (1)

we get,

=> 3 + y = 11

=> y = 8

Therefore,

original number = 10x + y

=> 10(3) + 8 = 38

original number = 38

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