Question

In a class test, the sum of Anamika's marks obtained in Maths and Science is 30. Had she got 2 marks more in Maths and 3 marks less in Science, the product of the marks would have been 210. Find the marks she got in the two subjects.

Hint:

To factor \(x^2 - 25x + 156\), look for factors of 156 that sum to 25. \(12 \times 13 = 156\) and \(12 + 13 = 25\).

Answer 1

Step 1: Understanding the Concept:
Set up a variable for one subject and express the other in terms of it. Form a quadratic equation from the given product condition.
Step 2: Detailed Explanation:
Let marks in Maths be \( x \). Then marks in Science \( = 30 - x \).
New Maths marks \( = x + 2 \).
New Science marks \( = (30 - x) - 3 = 27 - x \).
Product \( = 210 \):
\[ (x + 2)(27 - x) = 210 \]
\[ 27x - x^2 + 54 - 2x = 210 \implies -x^2 + 25x + 54 = 210 \]
\[ x^2 - 25x + 156 = 0 \]
Solving the quadratic:
\[ (x - 12)(x - 13) = 0 \implies x = 12 \text{ or } 13 \]
If Maths \( = 12 \), Science \( = 18 \).
If Maths \( = 13 \), Science \( = 17 \).
Step 3: Final Answer:
Her marks are (12, 18) or (13, 17).