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Real Numbers
RD Sharma Ch 01
CBSE_RD_SHARMA_CH01
Grade 10

Question:

Three sets of English, Hindi and Mathematics books have to be stacked in such a way that all the books are stored topic-wise and the height of each stack is the same. The number of English books is $96$, the number of Hindi books is $240$ and the number of Mathematics books is $336$. Assuming that the books are of the same thickness, determine the number of stacks of English, Hindi and Mathematics books.

Step-by-Step Solution

Key Concept: Find height of each stack $= \text{HCF}(96, 240, 336)$. Then divide each book count by HCF to get number of stacks.
Stepwise Solution:

Books in each stack $= \text{HCF}(96, 240, 336)$.
$96 = 2^5 \times 3$
$240 = 2^4 \times 3 \times 5$
$336 = 2^4 \times 3 \times 7$. [1.0 Mark]

$\text{HCF}(96, 240, 336) = 2^4 \times 3 = 16 \times 3 = 48$ books per stack. [1.0 Mark]

Number of English stacks $= 96 / 48 = 2$.
Number of Hindi stacks $= 240 / 48 = 5$.
Number of Math stacks $= 336 / 48 = 7$.
Total stacks $= 2 + 5 + 7 = 14$ stacks. [1.0 Mark]

Marking Scheme:

• Prime factorisation and evaluating HCF $= 48$: 2.0 Marks
• Calculating number of stacks for each subject (2, 5, 7) and total (14): 1.0 Mark

Correct Answer:
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