The consumption of diesel per hour of a
bus varies directly as square of its
speed. When the bus is traveling at 40
km/hr its consumption is 1 litre per hour.
If each litre cost Rs.40 and other
expenses per hour is Rs.40, then what
would be the minimum expenditure
required to cover a distance of 400 km?
Answers
Expenditure of 800 Rs. is required to cover a distance of 400 km.
Step-by-step explanation:
The bus is travelling at the speed = 40 km per hour
Time to cover a distance of 400 km =
= 10 hours
The consumption of diesel = 1 liter/hr
For 10 hours consumption of diesel = 10 × 1 = 10 liters
Cost of 1 liter diesel = Rs. 40
Cost of 10 liters diesel = 40 × 10 = 400 Rs.
Other expenses per hour = 40 Rs.
For 10 hours other expenses are = 40 × 10 = 400 Rs.
Total expenditure for 400 km = total cost of diesel + other total expenses
= 400 + 400
= 800 Rs.
Expenditure of 800 Rs. is required to cover a distance of 400 km.
Learn more word problem : https://brainly.in/question/1367530
The minimum expenditure required to cover a distance of 400 km is 800 liters.
Step-by-step explanation:
Given data:
Consumption per hr/Speed^2 = k = 1/1600
C = (1 / 1600) x Speed^2
Assume that time taken to cover 400 km is t hrs. Then Speed = 400/t
C = (1 / 1600) x (400 t) 2 C = ( 1 / 1600) x (400 / t)^2
C x t = 100 / t
C x t is the total fuel consumed.
We need to minimise 40 x C x t + 40 x t
40 x (100 / t + t) 40 x (100 / t+t)
Minimum value of (100/t + t) will be given when 100/t = t i.e. t = 10 (because the product of the two terms (100/t) x t = 100, a constant)
So the minimum value is 40 x (10 + 10) = 800
Hence the minimum expenditure required to cover a distance of 400 km is 800 liters.
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