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

Last updated at March 23, 2023 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

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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