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Mathematics · 2026 · 5 marks
CBSE 2026 · Region 2 · Set 3 · Q35
(a) 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,…
(a)
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.
OR
(b)
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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