In a competition, the ratio of the points scored by Team A and Team B was 3 : 4. If each team had scored 15 more points, the ratio of their points would have become 4 : 5. Find Team A's initial points.

1. A

   42

2. B

   40

3. C

   38

4. D

   45

Appeared in: NCL (Northern Coalfields Limited)-NO

Explanation

• The initial ratio of points for Team A to Team B is 3:4. This can be represented algebraically as 3x and 4x.
• When each team scores 15 more points, their new scores become (3x + 15) and (4x + 15).
• The new ratio is 4:5, which creates the equation (3x + 15) / (4x + 15) = 4/5.
• Solving this equation by cross-multiplication (5(3x + 15) = 4(4x + 15)) yields 15x + 75 = 16x + 60.
• Simplifying the equation gives x = 15.
• Team A's initial score is 3x, so substituting x = 15 gives 3 * 15 = 45.

Why Other Options Were Wrong

• Option A: If Team A's initial score was 42, then 3x = 42, which means x = 14. Team B's score would be 4 * 14 = 56. The new scores would be 42+15=57 and 56+15=71. The ratio 57:71 does not simplify to 4:5.
• Option B: The initial score for Team A must be a multiple of 3, according to the 3:4 ratio. 40 is not a multiple of 3, so it cannot be the correct answer.
• Option C: Similar to the option of 40, the initial score for Team A must be a multiple of 3. 38 is not divisible by 3, making it an impossible initial score based on the 3:4 ratio.

Related Visual

• Visual 1: No visual aid is required for this type of mathematical problem.

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving linear equations derived from ratio and proportion problems as background academic context rather than a clinical decision trigger.
• This question tests basic mathematical aptitude and logical reasoning.
• While not a direct clinical scenario, strong numeracy skills are essential for nurses in daily practice for tasks such as calculating medication dosages, titrating IV drips, and interpreting lab results.
• What if the question asked for Team B's final score? After finding x=15, Team B's initial score is 4x = 60. The final score would be 60 + 15 = 75.

How to Approach the Question

• First, read the problem carefully to identify the initial ratio (3:4) and the changes that occur (+15 points for each team).
• Represent the initial unknown quantities using a variable. Let the initial scores be 3x and 4x.
• Formulate new expressions based on the changes described: the new scores are (3x + 15) and (4x + 15).
• Set up an equation by equating the ratio of the new expressions to the new given ratio: (3x + 15) / (4x + 15) = 4/5.
• Solve the resulting linear equation for 'x' using cross-multiplication.
• Finally, use the value of 'x' to calculate the quantity the question asks for, which is Team A's initial score (3x).

Concept Tested & Keywords

• Concept Tested: Solving linear equations derived from ratio and proportion problems.
• Stem keywords: ratio, points scored, Team A, Team B, competition
• Lead-in keywords: Find

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