Arithmetic

Time, Speed & Distance

Medium

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?

115 km/h

120 km/h

121 km/h

116 km/h

✅ Correct Option: 2

Total journey = 200 km

Original average speed = 125 km/h (not used directly in calculation)

For the first 100 km, speed increases by 20% from original 125 km/h.

For the next 100 km, speed becomes (2/3)rd of the increased speed.

Original speed = 125 km/h

Increase by 20%:

Speed for first 100 km = 125 + (20% of 125)

$= 125 + \dfrac{20}{100} \times 125$

$= 125 + 25$

$= 150$ km/h

The speed decreases to (2/3)rd of the increased speed (150 km/h).

Speed for next 100 km = $\dfrac{2}{3} \times 150$

$= \dfrac{2 \times 150}{3}$

$= \dfrac{300}{3}$

$= 100$ km/h

Using Time = Distance ÷ Speed

For first 100 km:

Time $_1$ = $\dfrac{100}{150}$

$= \dfrac{2}{3}$ hour

For next 100 km:

Time $_2$ = $\dfrac{100}{100}$

$= 1$ hour

Total time = Time $_1$ + Time $_2$

$= \dfrac{2}{3} + 1$

$= \dfrac{2}{3} + \dfrac{3}{3}$

$= \dfrac{5}{3}$ hours

Average Speed = $\dfrac{\text{Total Distance}}{\text{Total Time}}$

$= \dfrac{200}{\dfrac{5}{3}}$

$= 200 \times \dfrac{3}{5}$

$= \dfrac{600}{5}$

$= 120$ km/h

Therefore, the new average speed is 120 km/h.

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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?

Solution

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