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The denominator of a fraction execeeds the numerator by 2. If 5 be added to the numerator the fraction increases by unity.?
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The denominator of a fraction execeeds the numerator by 2. If 5 be add...
Understanding the Problem
Let's define the variables involved in the fraction:
- Let the numerator be represented as "x".
- The denominator, as per the problem, is "x + 2" because it exceeds the numerator by 2.
Formulating the Fraction
The fraction can be expressed as:
- Fraction = x / (x + 2)
Condition Given in the Problem
According to the problem, when 5 is added to the numerator, the fraction increases by unity (1). This can be formulated as:
- (x + 5) / (x + 2) = (x / (x + 2)) + 1
Solving the Equation
To solve this equation, we can cross-multiply:
- (x + 5) = (x + 2) + (x)(x + 2)
This simplifies to:
- x + 5 = x + 2 + x^2 + 2x
- 5 = 2 + x^2 + 2x
- x^2 + 2x - 3 = 0
Factoring the Quadratic
Now, we need to factor the quadratic equation:
- (x + 3)(x - 1) = 0
This gives us two potential solutions:
- x = -3 or x = 1
Determining Valid Solutions
Since the numerator must be a non-negative integer, we select:
- x = 1
Final Values
- Numerator: 1
- Denominator: 3 (1 + 2)
Thus, the fraction is 1/3.
Verification
Adding 5 to the numerator gives us:
- New Fraction = (1 + 5) / (1 + 2) = 6 / 3 = 2
This confirms that the fraction indeed increases by 1.
Let's define the variables involved in the fraction:
- Let the numerator be represented as "x".
- The denominator, as per the problem, is "x + 2" because it exceeds the numerator by 2.
Formulating the Fraction
The fraction can be expressed as:
- Fraction = x / (x + 2)
Condition Given in the Problem
According to the problem, when 5 is added to the numerator, the fraction increases by unity (1). This can be formulated as:
- (x + 5) / (x + 2) = (x / (x + 2)) + 1
Solving the Equation
To solve this equation, we can cross-multiply:
- (x + 5) = (x + 2) + (x)(x + 2)
This simplifies to:
- x + 5 = x + 2 + x^2 + 2x
- 5 = 2 + x^2 + 2x
- x^2 + 2x - 3 = 0
Factoring the Quadratic
Now, we need to factor the quadratic equation:
- (x + 3)(x - 1) = 0
This gives us two potential solutions:
- x = -3 or x = 1
Determining Valid Solutions
Since the numerator must be a non-negative integer, we select:
- x = 1
Final Values
- Numerator: 1
- Denominator: 3 (1 + 2)
Thus, the fraction is 1/3.
Verification
Adding 5 to the numerator gives us:
- New Fraction = (1 + 5) / (1 + 2) = 6 / 3 = 2
This confirms that the fraction indeed increases by 1.
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The denominator of a fraction execeeds the numerator by 2. If 5 be added to the numerator the fraction increases by unity.?
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The denominator of a fraction execeeds the numerator by 2. If 5 be added to the numerator the fraction increases by unity.? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The denominator of a fraction execeeds the numerator by 2. If 5 be added to the numerator the fraction increases by unity.? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The denominator of a fraction execeeds the numerator by 2. If 5 be added to the numerator the fraction increases by unity.?.
The denominator of a fraction execeeds the numerator by 2. If 5 be added to the numerator the fraction increases by unity.? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The denominator of a fraction execeeds the numerator by 2. If 5 be added to the numerator the fraction increases by unity.? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The denominator of a fraction execeeds the numerator by 2. If 5 be added to the numerator the fraction increases by unity.?.
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