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Maths

Linear Equations in One Variable

Solving Linear Equations with Variable on Both Sides

The sum of the digits of a ...

MATHS

The sum of the digits of a two-digit number is 12. If the new number formed by reversing the digits is greater than the original number by 18, find the original number.

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ANSWER

Let x be the unit digit and y be tens digit.

Then the original number be 10x+y.

Value of the number with reversed digits is 10y+x.

As per question, we have

x+y=12 ....(1)

If the digits are reversed, the digits is greater than the original number by 18.

Therefore, 10y+x=10x+y+18

⇒9x−9y=−18 ....(2)

Multiply equation (1) by 9, we get

9x+9y=108 ....(3)

Add equations (2)and (3),

18x=90

⇒x=5

Substitute this value in equation (1), we get

5+y=12⇒y=7

Therefore, the original number is 10x+y=10×5+7=57..

Step-by-step explanation:

Given:-

the sum of digits of a two digit number is 12. if 8 is added to the number, the digits are reversed.(Note:- the digit 18 should be added to get the answer not 8)

To find:-

find the original number

Solution:-

Let the digits be X and Y

X is at 10's place

Y is at 1's place

Then the number =10X+Y

If the digits are reversed then the number

=10Y+X

Now, The sum of digits =12

=>X+Y=12------(1)

=>X=12-Y-------(2)

If 18 is added to the number the digits are reversed=

10X+Y+18=10Y+X

=>10X+Y+18-10Y-X=0

=>9X-9Y+18=0

=>9(12-Y)-9Y+18=0

=>108-9Y-9Y+8=0

=>126-18Y=0

=>18Y=126

=>Y=126/18

=>Y=7

and from (1)=>X=12-7=5

Answer:-

The digit at 10's place=5

The digit at 1's place=7

The original number=57

Check:-

Sum of 5and7=5+7=12

if 18 is added to 57 then 57+18=75

The digits are reversed