4 bells toll together at $9:00\text{ AM}$. They toll at intervals of $7, 8, 11$ and $12$ seconds respectively. How many times will they toll together again in the next $3$ hours?
Step-by-Step Solution
Key Concept: Find $\text{LCM}(7, 8, 11, 12)$. Total seconds in 3 hours $= 3 \times 3600 = 10800$. Number of times $= 10800 / \text{LCM}$.
$\text{LCM}(7, 8, 11, 12) = 2^3 \times 3 \times 7 \times 11 = 8 \times 3 \times 7 \times 11 = 1848$ seconds. [1.5 Marks]
Total time in seconds $= 3 \times 3600 = 10800$ seconds. [0.5 Mark]
Number of times $= 10800 / 1848 = 5.84 \Rightarrow 5$ times (excluding initial toll). [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Evaluating $\text{LCM} = 1848$ seconds: 1.5 Marks
Converting 3 hours to 10,800 seconds: 0.5 Mark
Calculating integer quotient $10800 / 1848 = 5$ times: 1.0 Mark
Correct Answer: