The sum of the digits of a number lying between 10 and 100 is 5. If the digits are re-versed, the number is increased by 9.find the number
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Step-by-step explanation:
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.
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