The sum of the digits of a two digit number is 10. If the digits are reversed, the new number is 72 more than the original. Find the number.
A
18
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B
19
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C
20
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D
21
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Solution
The correct option is B19 Let x and y be the two digit number x=tens digit y= units digit x+10y= reversed number Sum of the 2-digits, x+y=10 ---(1) As per the condition, we write the equation as x+10y=72+10x+y Grouping the like terms, 10y−y=10x−x+72 9y=9x+72 Both sides divide by 9, y=x+8 Substitute the y value in equation (1) x+x+8=10 2x=10−8 2x=2 x=1 Put the value of x in equation (1) 1+y=10 y=10−1 y=9 So, the number is 19.