The jogging track in a sports complex is $726$ metres in circumference. Deepak and his wife start from the same point and walk in opposite directions at $4.5$ km/hr and $3.75$ km/hr respectively. They will meet for the first time in

### Concept & Circular Track Relative Speed When two bodies start from the same point on a circular track and move in opposite directions, they meet when the sum of the distances they cover equals exactly one full circumference of the track. $$ \text{Meeting Time} = \frac{\text{Circumference}}{\text{Relative Speed}} $$ ### Step-by-Step Solution * **Given:** Track circumference = $726$ m. Deepak's speed = $4.5$ km/hr. Wife's speed = $3.75$ km/hr. They move in opposite directions. * **Calculation:** Relative speed = $4.5 + 3.75 = 8.25$ km/hr. * To make units compatible, convert the track distance into kilometers: $726 \text{ m} = 0.726 \text{ km}$. * Time taken to meet = $\frac{\text{Distance}}{\text{Relative Speed}} = \frac{0.726}{8.25}$ hours. * $\frac{0.726}{8.25} = 0.088$ hours. * The options are in minutes, so multiply by $60$: $0.088 \times 60 = 5.28$ minutes. ### Exam Strategy & Shortcut Convert speeds to m/min directly if preferred, but decimal division is fast here: $8.25$ km/hr = $\frac{8.25 \times 1000}{60}$ m/min = $137.5$ m/min. Time = $\frac{726}{137.5} = 5.28$ min. ### Common Pitfall Failing to convert the circumference from meters to kilometers (or speeds to meters/minute) before doing the division, resulting in massive magnitude errors. ### Final Answer Therefore, the correct answer is **$5.28$ min**.