Question

sum of two digits of a 2-digit number is 9. when 27 is subtracted from the number it is found that the digits have interchanged their places. find the number​

Answer 1

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Let us assume, x and y are the two digits of the two-digit number.

Therefore, the two-digit number = 10x+y and Reversed number = 10y+x

Given:

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

Also given: 10x + y − 27 = 10y+x

9x−9y = 27

x−y=3----------(2)

Adding equation (1) and equation (2)

2x=12

x=6

Hence,

The two-digit number =10x+y

⇒10 × 6 + 3 = 63.

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Answer 2

Given :-

The Sum of two digits of a 2-digit number is 9. when 27 is subtracted from the number it is found that the digits have interchanged their places.

To Find :-

Number

Solution :-

Let the number at one digit be x

Ten digit = (9 - x)

Original number = 10(9 - x) + x

Original number = 90 - 10x + x

Original number = 90 - 9x

When 27 is subtracted the number gets interchanged

Interchange number = 10(x) + 9 - x

Interchange number = 10x + 9 - x

Interchange number = 9x + 9

Original number - 27 = Interchange number

90 - 9x - 27 = 9x + 9

63 - 9x = 9x + 9

63 - 9 = 9x + 9x

54 = 18x

54/18 = x

3 = x

As,

Original number = 90 - 9x

Original number = 90 - 9(3)

Original number = 90 - 27

Original number = 63