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Solution


Q.

Rohan and Jayant are very close friends. They decided to go to Ranikhet with their families in separate cars. Rohan’s car travels at a speed of x km/h while Jayant’s car travels 10 km/h faster than Rohan’s car. Rohan took 2 hours more than Jayant to complete the journey of 300 km.

Based on the above information, answer the following questions:

 

(ii) What is the quadratic equation describing the speed of Rohan’s car
1 0  
2 1  
3 5  
4 3  

Ans.

(1)

Time taken by Rohan’s car to cover 300 km = 300/x hours
Time taken by Jayant’s car to cover 300 km = 300/(x + 10) hours

Since Rohan takes 2 hours more than Jayant to cover 300 km:
300/x – 300/(x + 10) = 2

⇒ 300[(x + 10) – x] / [x(x + 10)] = 2
⇒ 3000 / [x(x + 10)] = 2
⇒ x(x + 10) = 1500
⇒ x² + 10x – 1500 = 0

Hence, the quadratic equation describing the speed of Rohan’s car is x² + 10x – 1500 = 0