Q) Raj and Ajay are very close friends. Both the families decide to go to Ranikhet by their own cars. Raj’s car travels at a speed of x km/h while Ajay’s car travels 5 km/h faster than Raj’s car. Raj took 4 hours more than Ajay to complete the journey of 400 km.

Raj and Ajay are very close friends. Both the families decide to go to Ranikhet  CBSE important questions 2024

1. What will be the distance covered by Ajay’s car in two hours?
a) 2(x +5) km                  b) (x – 5) km         c) 2( x + 10) km          d) (2x + 5) km

2. Which of the following quadratic equation describe the speed of Raj’s car?
a) x2 – 5 x – 500 = 0                 b) x2 + 4x – 400 = 0
c) x2 + 5x – 500 = 0                  d) x2 – 4x + 400 = 0

3. What is the speed of Raj’s car?
a) 20 km/hour               b) 15 km/hour        c) 25 km/hour               d) 10 km/hour

4. How much time took Ajay to travel 400 km?
a) 20 hour                     b) 40 hour             c) 25 hour                    d) 16 hour

Ans: 1. Distance covered by Ajay’s car in two hours:

It is given that Speed of Raj’s car = X km/ h

and also given that Ajays car is 5 km/h faster

∴ Speed of Ajay’s car = x + 5 km/h

We know that the the distance D in km is given by:

D = S x T

where, S = Speed in km/h

and T = time taken in hr

Hence, the distance travelled by Ajay’s care in 2 hrs:

= 2 (X + 5) km/h

Therefore option (a) is correct.

2. Quadratic equation for the speed of Raj’s car:

It is given that the Raj took 4 hours more than Ajay to complete the journey of 400 km.

We know that the the time T in hrs is given by:

T = \frac{D}{S}

where, D = distance travelled in km

and S = Speed in km/h

∵ Speed of Raj’s Car = X km\h

∴ Time taken to travel 400 km by Raj’s car = \frac{400}{X}

∵ Speed of Raj’s Car = X + 5 km\h

∴ Time taken to travel 400 km by Ajay’s car = \frac{400}{X + 5}

By given condition, Time taken by Raj – Time taken by Ajay = 4 hrs

\frac{400}{X} - \frac{400}{X + 5} = 4

∴  400 [\frac{1}{\times} - \frac{1}{\times + 5}] = 4

∴  100 [\frac{\times + 5 - \times}{\times (\times + 5)}] = 1

∴  100 (5) = X (X +5)

∴  X2 + 5 X – 500 = 0

Therefore option (c) is correct.

3. Speed of Raj’s car:

To get value of X, we need to solve the quadratic equation:

X2 + 5 X – 500 = 0

X + 25 X – 20 X – 500 = 0

(X + 25) (X – 20) = 0

∴ X = – 25 and X = 20

Since value of speed can not be negative X \neq – 25; Therefore, X = 20 km/h

Therefore option (a) is correct.

4. Time taken by Ajay to travel 400 km:

Given that the speed of Ajay’s car = X + 5

∵ The speed of Raj’s car, X = 20 km/h

∴ The speed of Ajay’s car = X + 5 =  20 + 5 = 25 km/h

∴ Time taken to travel 400 km by Ajay’s car = \frac{400}{25} = 16 hrs

Therefore option (d) is correct.

इति समाधानम्

Please do press “Heart” button if you liked the solution.

Leave a Comment

Your email address will not be published. Required fields are marked *

Scroll to Top