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The average speed of a car is 20 km/hr more than the average speed of a bus. If the car takes 4 hours less than the bus to cover a distance of 300 km. Find the average speed of the car and the bus.

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Average speed of car and bus= 30 km/hrs and 30 km/hrs

Average speed of car and bus= 40 km/hrs and 30 km/hrs

Average speed of car and bus= 50 km/hrs and 50 km/hrs

Average speed of car and bus= 50 km/hrs and 30 km/hrs

answer is D.

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Detailed Solution

Concept- To solve this question of speed, distance and time we will use basic concept of speed distance formula,
That is

speed = \frac{distance}{time}

Here,
Formula of speed,

speed = \frac{distance}{time}

Therefore,

time = \frac{distance}{speed}

Then, let the speed of the bus

= x .

Then,speed of car

= x + 20 .

Now, average speed of bus,

speed = \frac{distance}{time}

When we put value we get

x + 20 = \frac{300}{\frac{300}{x} - 4}

Now, after doing cross multiplication,

x + 20 (\frac{300}{x} - 4) = 300

Then,

(x + 20) (300 - 4 x) = 300 x

300 x - 4 x^{2} + 6000 - 80 x = 300 x

4 x^{2} + 80 x = 6000

4 x^{2} + 80 x - 6000 = 0

Now, we will divide the equation by 4.

\frac{4 x^{2}}{4} + \frac{80 x}{4} - \frac{6000}{4} = 0

x^{2} + 20 x - 1500 = 0

Then, by using Factorization method,

x^{2} + 20 x - 1500 = 0

x^{2} + 50 x - 30 x - 1500 = 0

x (x + 50) - 30 (x + 50) = 0

(x - 30) (x + 50) = 0

x = 30 or x = - 50

As we can’t take speed as negative ,

therefore, x = 30

So,average speed of bus is

30 km / hrs .

And, the average speed of car is

x + 20 = 30 + 20

= 50

Therefore,average speed of car is

50 km / hrs

Hence, the correct option is 4.

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