Q). 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.

(Q 35 A – 30/2/3 – CBSE 2026 Question Paper)

Ans:

Step 1: Let’s consider, Anamika got X marks in Maths

By 1st condition, “the sum of marks obtained in Maths and Science is 30”.

∴ Marks in Science = 30 – X

Step 2: Now by 2nd condition, “Had she got 2 marks more in Maths and 3 marks less in Science, the product of the marks would have been 210”

∴ (X + 2) [(30 – X) – 3] = 210

∴ (X + 2) (27 – X) = 210

∴ 27 X – X ² + 54 – 2 X = 210

∴ 25 X – X ² – 156 = 0

∴ X ² – 25 X + 156 = 0

By mid term splitting, we get:

∴ X ² – 13 X – 12 X + 156 = 0

∴ X (X – 13) – 12 (X – 13) = 0

∴ (X – 13) (X – 12) = 0

∴ X = 13 and X = 12

Step 3: Here we have 2 solutions:

For X = 13, marks in Maths = 13, and Marks in Science = 30 – 13 = 17

For X = 12, marks in Maths = 12, and Marks in Science = 30 – 12 = 18

Therefore, Anamika scored either 13 and 17 marks, or 17 and 18 marks, in maths and science respectively.

Check: if marks in maths and science are 13 & 17, then 13 + 17 = 30 … it satisfies the 1st condition.
and (13 + 2) (17 – 3) = 15 x 14 = 210……it satisfies the 2nd condition.
Hence our 1st set of answer is correct.
Next, if marks in maths and science are 12 & 18, then 12 + 18 = 30 … it satisfies the 1st condition.
and (12 + 2) (18 – 3) = 14 x 15 = 210……it satisfies the 2nd condition.
Hence our 2nd set of answer is also correct.

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