Vijay has to go to office from home. He travels the first half of the distance at speed of 30 km/hr. For the remaining distance he travels at 10 km/hr for half the time and at 20 km/hr for the rest. Find his average speed.

40 km/hr

No worries! We‘ve got your back. Try BYJU‘S free classes today!

30 km/hr

No worries! We‘ve got your back. Try BYJU‘S free classes today!

20 km/hr

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

25 km/hr

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C
20 km/hr

Let's assume, time taken from A to B is $t_{1}$ , B to C is $t_{2}$ and C to D is $t_{2}$ .

$∴$ Total distance = AB + BC + CD

= $30 t_{1} + 10 t_{2} + 20 t_{2}$

Total time = $t_{1} + 2 t_{2}$

$∴ A v e r a g e s p e e d = \frac{30 t_{1} + 10 t_{2} + 20 t_{2}}{t_{1} + 2 t_{2}} = \frac{30 t_{1} + 30 t_{2}}{t_{1} + 2 t_{2}}$

But given, AB = BD = BC + CD

$∴ 30 t_{1} = 10 t_{2} + 20 t_{2}$

$\Rightarrow 30 t_{1} = 30 t_{2}$

$\Rightarrow t_{1} = t_{2}$

Average speed = $\frac{30 t_{1} + 30 t_{2}}{t_{1} + 2 t_{2}} = \frac{60 t_{1}}{3 t_{1}}$ = 20 km/hr.

Suggest Corrections

Similar questions

Q. If A train takes 1 hr to go from one station to another. It travels at a speed of 30 km hr for first half hour and at a speed of 50 km hr for the next half hour. Find the average speed of the train?

To go home on Christmas Eve, Vinay travels by Bus at 80 km/hr (yes Bangalore bus service is awesome) from office to Bangalore Airport for $(\frac{1}{3})^{3}$ of the total time. Then he travels by flight at 700 km/hr for next $(\frac{1}{3})^{3}$ of time to reach Chennai Airport. Then he takes a cab to his house which travels at 120 km/hr (since its midnight). Find his average speed for the entire journey.

Q. A car travels the first half of a distance between two places at a speed of

30 k m / h r

and the second half of the distance at

50 k m / h r .

. The average speed of the car for the whole journey is

Join BYJU'S Learning Program