The numerator of a fraction is 5 more than twice the denominator. Also, when 2 is added to the fraction, the numerator increases by 12. If the given fraction is squared and the numerator is divided by the denominator, then what will be the remainder?
- 1
- 0
- 3
- 2
The Correct Option is A
Solution and Explanation
- Let the numerator of the fraction be x and the denominator be y.
- According to the first condition, the numerator is 5 more than twice the denominator:
x = 2y + 5
- According to the second condition, when 2 is added to the fraction, the numerator increases by 12:
(x + 2)/y = x/y + 12
Step 1: Simplifying the Second Equation
Rearranging the second equation:
(x + 2)/y - x/y = 12
Since both terms have a common denominator:
[ (x + 2) - x ] / y = 12
Simplifying:
2 / y = 12
Step 2: Solving for y
Cross-multiplying gives:
y = 2 / 12 = 1 / 6
Since y must be an integer, this result indicates an incorrect step or condition. We need to revisit the conditions.
Step 3: Correcting the Approach
- Revisiting the first equation:
x = 2y + 5
Since there is a contradiction in the conditions, please confirm the correct second condition or any missing details for an accurate solution.
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