## Mathematics TERM II

## Quadratic Equations

## Class 10 Session 2021-2022

## Case Study Questions 04

**A Hill Station:** In the last summer, I enjoyed a tour to a hill station at Shimla. I was accompanied by my five friends and

enjoyed the natural beauties of mountains, rivers, streams, forests etc. The beginning of the tour was the most adventurous itself! How amazingly my group win the bet! Actually, the story is that my two friends along with me prefered train to go to Shimla, but other three were forcing for a car or a bus. At last the consensus was reached and we were divided ourselves in two groups of 3 each and started for Shimla at the same time. It was decided that the group who reach the destination first, would be declared as the winner, and runner up the group have to bear the expanses of the tour. I named my group, ‘Group A’ while the second group was named as ‘Group B’. Luckily we reached Shimla 1 hour before the Group-B and enjoyed the trip for absolutely FREE!! How thrilling it was the tour!

**Refer to Group-A**

1. An express train takes 1 hour less than a passenger train to travel 132 km between Delhi and Shimla (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is 11 km/hr more than that of the passenger train, the average speeds of the two trains will be

(a) 33 km/h, 44 km/hr

(b) 40 km/h, 45 km/h

(c) 30 km/h, 38 km/h

(d) 42 km/h, 62 km/h

(a) 33 km/h, 44 km/hr

2. An express train makes a run of 240 km at a certain speed. Another train whose speed is 12 km/hr less takes an hour longer to make the same trip. The speed of the express train will be

(a) 60 km/h

(b) 50 km/h

(c) 65 km/h

(d) 48 km/h

(a) 60 km/h

3. A journey of 192 km from Delhi to Shimla takes 2 hours less by a super fast train than that by an ordinary passenger train. If the average speed of the slower train is 16 km/hr less than that of the faster train, average speed of super fast train is

(a) 50 km/h

(b) 48 km/h

(c) 55 km/h

(d) 60 km/h

(b) 48 km/h

**Refer to Group-B**

4. A deluxe bus takes 3 hours less than a ordinary bus for a journey of 600 km. If the speed of the ordinary bus is 10 km/hr less than that of the deluxe bus, the speeds of the two buses will be

(a) 35 km/h, 42 km/h

(b) 42 km/h, 52 km/h

(c) 40 km/h, 50 km/h

(d) 30 km/h, 58 km/h

(c) 40 km/h, 50 km/h

5. A bus travels a distance of 300 km at a uniform speed. If the speed of the bus is increased by 5 km an hour, the journey would have taken two hours less. The original speed of the bus will be

(a) 20 km/h

(b) 15 km/h

(c) 22 km/h

(d) 25 km/h

(d) 25 km/h