Question:
At a bookstore, 'MODERN BOOK STORE' is flashed using neon lights. The words are individually flashed at the intervals of \( \frac{1}{2} \) s, \( \frac{1}{4} \) s and \( \frac{1}{8} \) s respectively, and each word is put off after a second. The least time after which the full name of the bookstore can be read again is:
At a bookstore, 'MODERN BOOK STORE' is flashed using neon lights. The words are individually flashed at the intervals of \( \frac{1}{2} \) s, \( \frac{1}{4} \) s and \( \frac{1}{8} \) s respectively, and each word is put off after a second. The least time after which the full name of the bookstore can be read again is:
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Use the least common multiple (LCM) to find the repeating intervals in time problems.
Updated On: Aug 4, 2025
- 49.5 s
- 73.5 s
- 1744.5 s
- 855 s
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The Correct Option is B
Solution and Explanation
The time intervals for each letter flashing are \( \frac{1}{2} \), \( \frac{1}{4} \), and \( \frac{1}{8} \). To find the least time, we calculate the least common multiple (LCM) of these intervals:
\[
\text{LCM} \left( \frac{1}{2}, \frac{1}{4}, \frac{1}{8} \right) = \frac{1}{8}.
\]
Thus, the full name of the bookstore can be read again after \( 73.5 \, \text{s} \).
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