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The bus fare between two cities in the hilly region is five times the square of the distance between them in rupees. The distance from city A to city B is 8 km by direct route. From city B to city A can be reached via city C and D, where the distance of city A and city C is 3 km, the distance from city C to city D is 3 km and the distance from city D to city B is 4 km. What is the difference between the expenditure on both the routes?

The bus fare between two cities in the hilly region is five times the square of the distance between them in rupees. The distance from city A to city B is 8 km by direct route. From city B to city A can be reached via city C and D, where the distance of city A and city C is 3 km, the distance from city C to city D is 3 km and the distance from city D to city B is 4 km. What is the difference between the expenditure on both the routes? Correct Answer Rs. 150

Given:

Fair = 5 × (Distance)2

Distance between city A and city B = 8 km

Distance between city A and city C = 3 km

Distance between city C and city D = 3 km 

Distance between city D and city B = 4 km

Formula Used:

Fair = 5 × (Distance)2

Calculations:

When bus goes from city A to city B

Distance between city A and city B = 8 km

⇒ Fair = 5 × (8)2 

⇒ Fair = Rs. 320      ----(1)

On return journey,

Distance between city A and city C = 3 km

⇒ Fair = 5 × (3)2 

⇒ Fair = Rs. 45

Distance between city C and city D = 3 km 

⇒ Fair = 5 × (3)2 

⇒ Fair = Rs. 45

Distance between city D and city B = 4 km

⇒ Fair = 5 × (4)2 

⇒ Fair = Rs. 80

Total fair in return journey = Rs. (45 + 45 + 80) 

⇒ Total fair in return journey = Rs. 170      ----(2)

Difference between the expenditure on both the routes = (1) - (2)

⇒ Difference between the expenditure on both the routes = Rs. (320 - 170)

⇒ Difference between the expenditure on both the routes = Rs. 150

∴ The Difference between the expenditure on both the routes is Rs. 150.

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