During a journey of 200 Km, the average speed of a car is 125 km/h. But if for the first 100 km, the driver increases its earlier average speed by 20% and then decreases it to its (2/3)rd for next 100 km. What will be the new average speed?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 120 km/h
1. Identify the given values
- Total Distance: $200 \text{ km}$
- Original Average Speed: $125 \text{ km/h}$
2. Calculate the speed for the first 100 km
The driver increases the earlier average speed ($125 \text{ km/h}$) by $20\%$.
- New Speed ($v_1$): $125 + (20\% \text{ of } 125) = 125 \times 1.2 = \mathbf{150 \text{ km/h}}$
- Time Taken ($t_1$): $\text{Distance} / \text{Speed} = 100 / 150 = \mathbf{\frac{2}{3} \text{ hours}}$ (approx. $40$ minutes)
3. Calculate the speed for the next 100 km
The driver then decreases the current speed to its $\frac{2}{3}$rd.
- New Speed ($v_2$): $\frac{2}{3} \times 150 = \mathbf{100 \text{ km/h}}$
- Time Taken ($t_2$): $\text{Distance} / \text{Speed} = 100 / 100 = \mathbf{1 \text{ hour}}$
4. Calculate the new average speed
The average speed for the whole journey is the total distance divided by the total time.
- Total Time: $t_1 + t_2 = \frac{2}{3} + 1 = \mathbf{\frac{5}{3} \text{ hours}}$
- New Average Speed: $\frac{\text{Total Distance}}{\text{Total Time}} = \frac{200}{5/3} = 200 \times \frac{3}{5}$
$\text{New Average Speed} = 40 \times 3 = \mathbf{120 \text{ km/h}}$
Conclusion
The new average speed of the car is 120 km/h.