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Mathematics · 2025 · 3 marks
CBSE 2025 · Region 1 · Set 2 · Q27
Three sets of Physics, Chemistry and Mathematics books have to be stacked in such a way that all the books are stored subject-wise and the height of…
Three sets of Physics, Chemistry and Mathematics books have to be stacked in such a way that all the books are stored subject-wise and the height of each stack is the same. The number of Physics books is $\displaystyle 144$, the number of Chemistry books is $\displaystyle 180$ and the number of Mathematics books is 192. Assuming that the books are of same thickness, determine the number of stacks of Physics, Chemistry and Mathematics books.
Marking-scheme solution
\[\begin{aligned}
& 144=2^{4} \times 3^{2} \\
& 180=2^{2} \times 3^{2} \times 5 \\
& 192=2^{6} \times 3 \\
& H C F=2^{2} \times 3=12
\end{aligned}
\]
Number of stacks of Physics Books \(\displaystyle =\frac{144}{12}=12\)
Number of stacks of Chemistry Books \(\displaystyle =\frac{180}{12}=15\)
Number of stacks of Mathematics Books \(\displaystyle =\frac{192}{12}=16\)
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