The sum of the digits of a two-digit number is 3. If the digits are reversed, the new number increased by 3 is twice the original number. Then the original number is: (a) 12 (b) 30 (c) 21 (d) none of these.
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option c) 21
Step-by-step explanation:
Given statements:
- Sum of the digits of a two-digit number is 3
- New number increased by 3 is twice the original number.
Let the two digits be x and y.
The sum of the two digits is equal to 3 this implies that:
x + y = 3 [Equation 2]
The original number is 10x + y, and reversing the digits would be equal to 10y + x.
So according to second statement,
10y + x + 3 = 2( 10x + y )
10y + x + 3 = 20x + 2y
8y - 19x = -3 [Equation 2]
Sloving Equation 1 and Equation 2 we get the values of x and y as x = 2 and y = 1.
So the original number 10x + y = 10(2) + 1 = 20 + 1 = 21
Option c) 21 is the correct answer.
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