The usual average speed of a car on particular stretch of road is 75 km/hr. On a particular day, the average speed was `12%` less than the usual, as a result of which the time taken was 18 minutes more. How is the stretch of road in kilometers ?

Options

A. 155
B. 176
C. 165
D. 150

Answer

To solve the problem step by step, we need to find the length of the stretch of road based on the given average speeds and the additional time taken.

### Step 1: Determine the reduced speed
The usual average speed of the car is 75 km/hr. The average speed on the particular day is 12% less than the usual speed.

\[ \text{Reduced Speed} = \text{Usual Speed} - \left( \frac{12}{100} \times \text{Usual Speed} \right) \]

Calculating the reduced speed:

\[ \text{Reduced Speed} = 75 - \left( \frac{12}{100} \times 75 \right) = 75 - 9 = 66 \text{ km/hr} \]

### Step 2: Establish the relationship between distance, speed, and time
Let the distance of the stretch of road be \( D \) kilometers. The time taken to cover this distance at the usual speed is:

\[ \text{Time at Usual Speed} = \frac{D}{75} \text{ hours} \]

The time taken to cover this distance at the reduced speed is:

\[ \text{Time at Reduced Speed} = \frac{D}{66} \text{ hours} \]

### Step 3: Set up the equation based on the time difference
According to the problem, the time taken at the reduced speed is 18 minutes more than the time taken at the usual speed. We need to convert 18 minutes into hours:

\[ 18 \text{ minutes} = \frac{18}{60} = 0.3 \text{ hours} \]

Now, we can set up the equation:

\[ \frac{D}{66} = \frac{D}{75} + 0.3 \]

### Step 4: Solve the equation for \( D \)
To solve for \( D \), we first eliminate the fractions by multiplying through by the least common multiple of 66 and 75, which is 3300:

\[ 3300 \left( \frac{D}{66} \right) = 3300 \left( \frac{D}{75} \right) + 3300 \times 0.3 \]

This simplifies to:

\[ 50D = 44D + 990 \]

Now, subtract \( 44D \) from both sides:

\[ 50D - 44D = 990 \]

\[ 6D = 990 \]

Now, divide both sides by 6:

\[ D = \frac{990}{6} = 165 \]

### Final Answer
The length of the stretch of road is **165 kilometers**.

---