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: Let the Marks be
Let marks in Maths = x
Then marks in Science = 30 − x

Step 2: Apply Given Change
New Maths marks = x + 2
New Science marks = (30 − x) − 3
= 27 − x

Given product = 210

(x + 2)(27 − x) = 210

Step 3: Expand and Simplify
27x − x² + 54 − 2x = 210

−x² + 25x + 54 = 210

−x² + 25x − 156 = 0

Multiply by −1:
x² − 25x + 156 = 0

Factorise:
(x − 12)(x − 13) = 0

x = 12 or x = 13

Step 4: Find Corresponding Science Marks
If x = 12,
Science = 18

If x = 13,
Science = 17

Final Answer:
Marks are (12, 18) or (13, 17).