There are two towns Ramgarh and Arjangarh which are separated by a hill. The people of one town have to travel on a zig-zag road which goes over the hill so as to reach the other town. Gaurav is a student of class IX in Ramgarh. Onnce Gaurav went from Ramgrah to Arjangarh on a scooter with his father. Driving at a constant speed of 50km/h on the hilly road, it took exactly 30 minute to reach Arjangarh. One day Gaura told his father that if a straight tunnel could be dug through the hill, then it would become very easy for the people of two towns to visit each other. keeping this is mind, Gaurav invited the people of both the towns and took a delegation to the Collector's office. This delegation demanded the construction of a straight tunnel road through the hill. Gaurav explained the various advantages of connecting Ramgarh and Arjangarh through a tunnel road in the hill. The collector liked the idea and a straight tunnel road was constructed after some time. One day Gaurav went from Ramgarh to Arjangarh through the straight tunnel road on the scooter with his father. Driving at a constant speed of 50 km/h, it took them just 12 minutes to reach Arjangarh. Both, Gaurav and his father were very happy.
(a) What was the distance covered by Gaurav on going from Ramgarh to Arjangarh by travelling on road over the hill?
(b) What is the distance covered by Gaurav on going from Ramgarh to Arjangarh by travelling on straight tunnel road/
(c) How much less distance is to be covered now in going through the tunnel than on going over the hill?
(d) What is the displacement of Gaurav from Ramgarh on reaching Arjangarh?
(e) State two advantages of construction of the tunnel road for the people of two towns.
(f) What values are displayed by Gaurav in this episode?

Explanation

Distance covered (over the hill) = Speed `xx` Time taken
`= 50 xx (30)/(60km) (30 min = (30)/(60)h)`
`= 25km`
(b) Distance covered (on tunnel road) = Speed `xx` Time taken
`=50 xx (12)/(60)km (12 min =(12)/(60)h)`
`= 10 km`
(c) Less distance covered `= 25 km - 10 km`
`= 15km`
(d) Displacement = 10 km (It is the shortest, straight line distance between the two towns)
(e) (i) Saving of fuel (because now less fuel is consumed to travel only 10 km distance as compared to 25 km earlier)
(ii) Saving of time (because now less time is taken in travelling 10 km distance than 25km earlier)
(f) The values displayed by Gaurav are (i) Responsible citizen (ii) Knowledge of distance travelled and displacement (ii) Application of knowledge in real-life siutations (iv) Conservation of fuel, and (v) Saving people's time.