The speed of a bike is 10\% less than the speed of a car. The bike takes 2 hours more than the car to cover a distance of 180 km, while the car covers 300 km in the same scenario. What is the speed of the bike in km/hr?

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**Solution:**

1. Let the speed of the car be $10x$ km/hr.

2. Since the bike's speed is 10\% less than the car's speed, the bike's speed is:
   $$10x 	imes \frac{90}{100} = 9x 	ext{ km/hr}$$

3. Time taken by the car to cover 300 km:
   $$\frac{300}{10x} = \frac{30}{x} 	ext{ hours}$$

4. Time taken by the bike to cover 180 km:
   $$\frac{180}{9x} = \frac{20}{x} 	ext{ hours}$$

5. According to the problem, the bike takes 2 hours more than the car:
   $$\frac{20}{x} - \frac{30}{x} = 2$$

6. Simplify the equation:
   $$\frac{20 - 30}{x} = 2 \implies \frac{-10}{x} = 2 \implies x = -\frac{10}{2} = -5$$

Since speed cannot be negative, reverse the order:
   $$\frac{30}{x} - \frac{20}{x} = 2 \implies \frac{10}{x} = 2 \implies x = 5$$

7. Therefore, speed of the bike:
   $$9x = 9 	imes 5 = 45 	ext{ km/hr}$$

**Answer:** $45$ km/hr

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