Two guns were fired from the same place at an interval of 8 minutes, A person approaching the place observes that 5 minutes 52 seconds have elapsed between the hearing of the sound of the two guns. If the velocity of the sound is 330 m/sec, the man was approaching the place at what speed (in km/hr)?

### Concept & Logic This is a classic relative speed problem involving sound. The distance that sound would have traveled in the remaining time of the firing interval is equal to the total distance the approaching man traveled during his observed elapsed time. *(Note: There is a typographical error in the original printed question where "8 minutes" is written instead of the mathematically intended "6 minutes". The solution below assumes 6 minutes to align with standard logic and the provided options).* ### Step-by-Step Solution * **Given:** Intended time interval of guns = $6$ minutes. Time elapsed for the moving observer = $5$ min $52$ sec. Speed of sound = $330$ m/s. * **Calculation:** Convert the time values into seconds. * Intended firing interval = $6 \times 60 = 360$ seconds. * Time elapsed heard by the observer = $(5 \times 60) + 52 = 352$ seconds. * Difference in time = $360 - 352 = 8$ seconds. * The distance the sound wave would have traveled in those "missing" $8$ seconds = $330 \text{ m/s} \times 8 \text{ s} = 2640$ m. * The approaching man must have traveled this exact same distance ($2640$ m) over his entire traveling duration between hearing the shots ($352$ seconds). * Speed of the man in m/s = $\frac{2640}{352} = 7.5$ m/s. * To convert m/s to km/hr, multiply by $\frac{18}{5}$: $7.5 \times \frac{18}{5} = 27$ km/hr. ### Exam Strategy & Shortcut Use the direct proportionality formula for these problems: $\text{Speed of Man} = \text{Speed of Sound} \times \left( \frac{\text{Actual Interval} - \text{Heard Interval}}{\text{Heard Interval}} \right)$. Assuming the intended $6$ minutes: $\text{Speed} = 330 \times \left(\frac{360 - 352}{352}\right) = 330 \times \frac{8}{352} = 7.5$ m/s $\implies 27$ km/hr. ### Common Pitfall Using the typo value of "$8$ minutes" blindly will yield $120$ m/s ($432$ km/hr), which is completely absent from the options. Recognizing standard typographical errors in competitive exam questions is an essential troubleshooting skill. ### Final Answer Therefore, the correct answer is **$27$**.