Amit covers a certain distance on his bike at a speed of 40 km/h in 15 min. If he wants to cover the same distance in 12 min, then what should his speed be?

Options

A. 60 km/h
B. 50 km/h
C. 72 km/h
D. 32 km/h

Answer

To solve the problem step by step, let's break it down:

### Step 1: Convert the time from minutes to hours
Amit covers a distance in 15 minutes. Since speed is given in km/h, we need to convert minutes to hours.

\[ \text{Time in hours} = \frac{15 \text{ minutes}}{60} = \frac{1}{4} \text{ hours} \]

**Hint:** Remember that 1 hour = 60 minutes, so to convert minutes to hours, divide by 60.

### Step 2: Calculate the distance covered
Using the formula for distance, which is:

\[ \text{Distance} = \text{Speed} \times \text{Time} \]

Given that the speed is 40 km/h and the time is \(\frac{1}{4}\) hours:

\[ \text{Distance} = 40 \text{ km/h} \times \frac{1}{4} \text{ hours} = 10 \text{ km} \]

**Hint:** To find distance, multiply the speed by the time taken.

### Step 3: Determine the new time in hours
Amit wants to cover the same distance of 10 km in 12 minutes. We need to convert 12 minutes to hours:

\[ \text{Time in hours} = \frac{12 \text{ minutes}}{60} = \frac{1}{5} \text{ hours} \]

**Hint:** Again, convert minutes to hours by dividing by 60.

### Step 4: Calculate the required speed
Now, we can use the distance formula again to find the required speed. We know the distance is 10 km and the time is \(\frac{1}{5}\) hours:

\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{10 \text{ km}}{\frac{1}{5} \text{ hours}} = 10 \text{ km} \times 5 = 50 \text{ km/h} \]

**Hint:** To find speed, divide the distance by the time taken.

### Conclusion
Amit needs to travel at a speed of **50 km/h** to cover the same distance in 12 minutes.

**Final Answer:** 50 km/h