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

Last updated at Oct. 1, 2019 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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.