A racing car going at an average speed of 108 km/hr takes 15 minutes to complete a lap on a racing track. By how much should it increase its speed (in km/hr) to complete the lap in 12 minutes ?

Options

A. 24
B. 21
C. 27
D. 30

Answer

To solve the problem step by step, we need to determine how much the racing car's speed should be increased to complete the lap in 12 minutes instead of 15 minutes.

### Step 1: Calculate the distance of the lap using the initial speed and time.
- The initial speed of the car is 108 km/hr.
- The time taken to complete the lap is 15 minutes. We need to convert this time into hours for consistency with the speed unit (km/hr).

\[ \text{Time in hours} = \frac{15 \text{ minutes}}{60} = 0.25 \text{ hours} \]

- Now, we can calculate the distance using the formula:

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

\[ \text{Distance} = 108 \text{ km/hr} \times 0.25 \text{ hr} = 27 \text{ km} \]

### Step 2: Calculate the new speed required to complete the lap in 12 minutes.
- The new time to complete the lap is 12 minutes, which we also convert to hours:

\[ \text{Time in hours} = \frac{12 \text{ minutes}}{60} = 0.2 \text{ hours} \]

- Now, we can calculate the new speed required using the same distance:

\[ \text{New Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{27 \text{ km}}{0.2 \text{ hr}} = 135 \text{ km/hr} \]

### Step 3: Calculate the increase in speed.
- The original speed was 108 km/hr, and the new speed required is 135 km/hr. To find the increase in speed:

\[ \text{Increase in Speed} = \text{New Speed} - \text{Original Speed} = 135 \text{ km/hr} - 108 \text{ km/hr} = 27 \text{ km/hr} \]

### Final Answer:
The racing car should increase its speed by **27 km/hr** to complete the lap in 12 minutes.

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