Question 15 - CBSE Class 10 Sample Paper for 2019 Boards - Solutions of Sample Papers for Class 10 Boards

Last updated at April 16, 2024 by Teachoo

Question 15

Places A and B are 80 km apart from each other on a highway. A car starts from A and another from B at the same time. If they move in same direction they meet in 8 hours and if they move towards each other they meet in 1 hour 20 minutes. Find the speed of cars.

Question 15
Places A and B are 80 km apart from each other on a highway. A car starts from A and another from B at the same time. If they move in same direction they meet in 8 hours and if they move towards each other they meet in 1 hour 20 minutes. Find the speed of cars.
Let the speed of first car be x km/hr
and speed of second car be y km/hr
If travelling in same direction
Time = 8 hours
Distance travelled by 1st car = AC
Distance travelled by 2nd car = BC
Difference of distance travelled = AC – BC
= (AB + BC) – BC
= AB
= 80 km
Therefore,
Distance travelled by 1st car – Distance travelled by 2nd car = 80 km
Speed = (𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 )/𝑇𝑖𝑚𝑒
Distance = Speed × Time
8x – 8y = 80
8 (x – y) = 80
x – y = 80/8
x – y = 10
…(1)
1 mark
If travelling in opposite direction
Time = 1 hours 20 minutes
= 1 + 20/60 hours
= 1 + 1/3 = 4/3 hours
Distance travelled by 1st car = AC
Distance travelled by 2nd car = BC
Now,
Total distance travelled = AC + BC
= AB
= 80 km
Therefore,
Distance travelled by 1st car + Distance travelled by 2nd car = 80 km
Speed = (𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 )/𝑇𝑖𝑚𝑒
Distance = Speed × Time
4/3x + 4/3y = 80
4/3 (x + y) = 80
x + y = 80 × 3/4
x + y = 60 …(2) 1 mark
Thus, our equations are
x – y = 10 …(1)
x + y = 60 …(2)
Adding (1) & (2)
(x – y) + (x + y) = 10 + 60
2x = 70
x = 70/2
x = 35
Putting value of x in (2)
x + y = 60
35 + y = 60
y = 60 – 35
y = 25
So,
Speed of first car = x = 35 km/hr
Speed of second car = 25 km/hr
1 mark

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

Hi, it looks like you're using AdBlock :(

Displaying ads are our only source of revenue. To help Teachoo create more content, and view the ad-free version of Teachooo... please purchase Teachoo Black subscription.

Please login to view more pages. It's free :)

Teachoo gives you a better experience when you're logged in. Please login :)

Solve all your doubts with Teachoo Black!

Teachoo answers all your questions if you are a Black user!