An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in $1\frac{2}{3}$ hours, it must travel at a speed of

### Concept & Distance Formula For a fixed distance, the product of speed and time remains constant. Calculate the total distance first, then use it to find the new speed. $$D = S_1 \times T_1 = S_2 \times T_2$$ ### Step-by-Step Solution * Find total distance: $\text{Speed} = 240$ kmph, $\text{Time} = 5$ hours. * Distance = $240 \times 5 = 1200$ km. * New time required = $1\frac{2}{3}$ hours = $\frac{5}{3}$ hours. * Let the required speed be $S$. * $S \times \frac{5}{3} = 1200$ * $S = 1200 \times \frac{3}{5}$ * $S = 240 \times 3 = 720$ kmph. ### Exam Strategy & Shortcut Using $S_1 \times T_1 = S_2 \times T_2$: $240 \times 5 = S_2 \times \frac{5}{3}$. The 5s cancel out immediately across the equation. $S_2 = 240 \times 3 = 720$. This calculation can easily be done in under 10 seconds mentally. ### Common Pitfall Incorrectly converting the mixed fraction $1\frac{2}{3}$ into a decimal and struggling with repeating decimals ($1.666...$) during division. Always use improper fractions for these calculations. ### Final Answer Therefore, the correct answer is **720 kmph**.