Santosh’s car gives 5 km more per litre of diesel when driven on the highway in comparison to city drive. On a recent trip, Santosh drove 30 km on the highway and 130 km in the city consuming a total of 15 litres of diesel in the process. How many km/litre does Santosh’s car run in the city?a)10 km/litreb)12 km/litrec)13 km/litred)14 km/litreCorrect answer is option 'A'. Can you explain this answer?

Question

Answer

Let the mileage of Santosh's car be n km/litre of diesel when driven in the city and (n+5) km/litre when driven on the highway. Translating the given information in to an equation, we can write

⇒ 3n² + 17n – 130 = 0

Which gives n = 10 or n = -13/3

Hence we can say that Santosh's car runs 10 km/litre in the city.

Answer

To solve this problem, let's assume that the car's mileage in the city is x km/litre.

Given that the car gives 5 km more per litre of diesel when driven on the highway, the mileage on the highway can be expressed as (x + 5) km/litre.

Now, let's calculate the total distance traveled by the car.
The car traveled 30 km on the highway and 130 km in the city, so the total distance is 30 + 130 = 160 km.

Since the car consumed a total of 15 litres of diesel, we can calculate the average mileage of the car as follows:
Average mileage = Total distance / Total fuel consumed
= 160 km / 15 litres
= 10.67 km/litre

Now, we can set up an equation to find the mileage in the city.
Let's assume the car's mileage in the city is x km/litre.
The car traveled 30 km on the highway, which gives (30 / (x + 5)) litres of fuel consumed.
The car traveled 130 km in the city, which gives (130 / x) litres of fuel consumed.

Since the total fuel consumed is 15 litres, we have the equation:
(30 / (x + 5)) + (130 / x) = 15

Now, let's solve this equation to find the value of x.

(30 / (x + 5)) + (130 / x) = 15
Multiplying both sides of the equation by x(x + 5) to eliminate the fractions, we get:
30x + 150 + 130(x + 5) = 15x(x + 5)
30x + 150 + 130x + 650 = 15x^2 + 75x
160x + 800 = 15x^2 + 75x
15x^2 + 75x - 160x - 800 = 0
15x^2 - 85x - 800 = 0
Dividing both sides of the equation by 5, we get:
3x^2 - 17x - 160 = 0

This quadratic equation can be factored as:
(3x + 16)(x - 10) = 0

Setting each factor equal to zero, we get:
3x + 16 = 0 or x - 10 = 0

Solving these equations, we find:
x = -16/3 or x = 10

Since the mileage cannot be negative, the value of x is 10 km/litre.

Therefore, the car runs at 10 km/litre in the city.

Hence, the correct answer is option A) 10 km/litre.

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