Question

a number between 10 and 100 is 5 times the sum of its digit if 9 is added to it the digits are reversed find the number​

Answer 1

Let x be the first digit.

Let y be the second digit.

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5(x+y)=10x+y ...(i)

5x+5y=10x+y

5y-y=10x-5x

4y=5x ...(ii)

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The 10x+y is because the x digit is in the ten's column and it is worth more.

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10x+y+9=10y+x ...(iii)

10x-x+9=10y-y

9x+9=9y

9(x+1)=9y

x+1=y ...(iv)

substitute x+1=y into (ii)

4(x+1)=5x ...(v)

4x+4=5x

4=5x-4x

x=4

substitute x=4 into (ii)

4y=5(4)

4y=20

y=20/4

y=5

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The first digit is 4. The second digit is 5.

The number is 45.