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. Ankita travels 14 km to her home partly by rickshaw and partly by bus. She takes half an hour if she travels 2 km by rickshaw, and the remaining distance by bus. On the other hand, if she travels 4 km by rickshaw and the remaining distance by bus, she takes 9 minutes longer. Find the speed of the rickshaw and the bus in km/hr respectively.

Q. Pankaj went to the post-office at the speed of 60 km/hr. While returning to his home, he covered half of the distance at the speed of 10 km/hr, but suddenly he realized that he was getting late so he increased the speed and reached the home by covering rest half of the distance at the speed of 30 km/hr. The average speed of the Pankaj in the whole length of journey is :

If a car travels first 40km at speed of 20km/h and next 80km at a speed of 40km/h. What is the average speed of car for entire journey?

The distance between two milestones is 230 km and two cars start simultaneously from the milestones in opposite directions. The distance between them after three hours is 20 km. If the speed of one car is less than that of other by 10 km/hr, find the speed of each car.

The distance between two milestones is 230 km and two cars start simultaneously from the milestones and start moving towards each other.. The distance between them after three hours is 20 km. If the speed of one car is less than that of other by 10 km/hr, find the speed of both the cars.

Join BYJU'S Learning Program