Question

The average speed of cars and bikes together is 80 km/h. If the average speed of the bike is 90 km/h and the average speed of the cars is 75 km/h, then find the ratio of the number of cars to the number of bikes.

• A. 2 : 3
• B. 1 : 2
• C. 2 : 1
• D. 3 : 2

Answer 1

The correct option is C 2 : 1

Given,
The average speed of cars = 75 km/h
The average speed of bikes = 90 km/h
Average speed of cars and bikes together = 80km/h

Let, the number of bikes be $x$
and the number of cars be $y.$

According to question,

$\frac{\text{(Sum of the speeds of bikes)}}{x}=90$

$\therefore \text{Speed of x bikes}=90x$

$Also,\frac{\text{(Sum of speed of cars)}}{y}=75$

$\therefore \text{Speed of y cars}=75y$

$\text{and}\frac{\text{((Sum of speeds of bikes)+(Sum of speed of cars))}}{(x+y)}=80$

$\Rightarrow \frac{90x+75y}{x+y}=80$
$\Rightarrow 90x+75y=80x+80y$
$\Rightarrow 10x=5y$
$\Rightarrow 2x=y$
$\Rightarrow \frac{2}{1}=\frac{y}{x}$

Therefore, the ratio of the number of cars to the number of bikes is 2:1.