CBSE Class 10 Maths Sample Paper 2019 | Q15

This 2019 CBSE class 10 Maths sample question paper 3 mark question is from Linear Equations. A word problem. Frame a pair of linear equations in two variables from the information given and solve the equations to find the speed of the 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.

Video Explanation

Explanatory Answer | CBSE Sample Paper 2019 Question 15

Let the speed of car A be x km/h. Let the speed of car B be y km/h. Let x > y
Distance between the two cars is 80 km.

Case 1: Same Direction | Time taken to meet = 8 hours

Because x > y, car A is 80 km behind car B when they travel in the same direction.
So, car A would have travelled 80 more km than car B when they meet.
In 8 hours car A travels 8x km. In 8 hours car B travels 8y km.
Difference in distance travelled by the cars = 8x – 8y = 80
x – y = 10 .....(1)

Case 2: Opposite Directions | Moving towards each other | Time taken to meet = 1 hour 20 min

Distance travelled by car A = time × speed = \\frac{4}{3}) x km
distance travelled by car B = time × speed = \\frac{4}{3}) y km
Distance travelled by car A + distance travelled by car B = 80 km
\\frac{4}{3})x + \\frac{4}{3}) y = 80
x + y = 80 × \\frac{4}{3})
x + y = 60 ..... (2)

Add 1 and 2:
2x = 70
x = 35 km/h
Substitute the value of x in (1):
35 – y = 10
y = 25 km/h