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Mathematics · 2026 · 5 marks
CBSE 2026 · Region 2 · Set 3 · Q35
In a class test, the sum of Anamika's marks obtained in Maths and Science is 30. Had she got $\displaystyle 2$ marks more in Maths and $\displaystyle 3$ marks less in Science, the product of the marks would have been 210. Find the marks she got in the two subjects.The length of hypotenuse (in cm) of a right-angled triangle is $\displaystyle 6$ cm more than twice the length of its shortest side. If the length of its third side is $\displaystyle 6$ cm less than thrice the length of its shortest side, find the dimensions of the triangle.
In a class test, the sum of Anamika's marks obtained in Maths and Science is 30. Had she got $\displaystyle 2$ marks more in Maths and $\displaystyle 3$ marks less in Science, the product of the marks would have been 210. Find the marks she got in the two subjects.
The length of hypotenuse (in cm) of a right-angled triangle is $\displaystyle 6$ cm more than twice the length of its shortest side. If the length of its third side is $\displaystyle 6$ cm less than thrice the length of its shortest side, find the dimensions of the triangle.
Marking-scheme solution
Let the marks obtained in Maths be x
Then the marks obtained in Science \(\displaystyle =30-\mathrm{x}\)
\(\displaystyle (\mathrm{x}+2)(30-\mathrm{x}-3)=210\)
\(\displaystyle \Rightarrow \mathrm{x}^{2}-25 \mathrm{x}+156=0\)
\(\displaystyle \Rightarrow(\mathrm{x}-13)(\mathrm{x}-12)=0\)
\(\displaystyle \therefore \mathrm{x}=13, \mathrm{x}=12\)
Either marks in Maths and Science are $\displaystyle 13$ and $\displaystyle 17$ respectively
or marks in Maths and Science are $\displaystyle 12$ and $\displaystyle 18$ respectively
Let the shortest side be x cm
Then hypotenuse \(\displaystyle =(2 \mathrm{x}+6) \mathrm{cm}\)
and the third side \(\displaystyle =(3 \mathrm{x}-6) \mathrm{cm}\)
\(\displaystyle \mathrm{x}^{2}+(3 \mathrm{x}-6)^{2}=(2 \mathrm{x}+6)^{2}\)
\(\displaystyle \Rightarrow 6 \mathrm{x}^{2}-60 \mathrm{x}=0\)
\(\displaystyle \Rightarrow 6 \mathrm{x}(\mathrm{x}-10)=0\)
\(\displaystyle \Rightarrow \mathrm{x}=0, \mathrm{x}=10\)
\(\displaystyle \mathrm{x}=0\) (rejected)
\(\displaystyle \therefore \mathrm{x}=10\)
∴ shortest side \(\displaystyle =10 \mathrm{~cm}\)
and hypotenuse \(\displaystyle =26 \mathrm{~cm}\)
and third side \(\displaystyle =24 \mathrm{~cm}\)
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CBSE Class 10 Mathematics past-paper question from the 2026board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.