Amit goes to his office by car at the speed of 80 km/hr and reaches 15 minutes earlier. If he goes at the speed 60 km/hr, he reaches 15 minutes late. What will be the speed (in km/hr) of the car to reach on time?

Options

A. A. `66 2/7`
B. B. `67 4/7`
C. C. `68 4/7`
D. D. `69 4/7`

Answer

To solve the problem step-by-step, we can follow these steps:

### Step 1: Define Variables
Let the distance to Amit's office be \( D \) kilometers and the actual time taken to reach on time be \( T \) hours.

### Step 2: Set Up Equations
1. When Amit travels at 80 km/hr, he reaches 15 minutes (or \( \frac{15}{60} = \frac{1}{4} \) hours) early. Therefore, the time taken is:
\[ \text{Time} = T - \frac{1}{4} \]
The equation for distance is:
\[ D = 80 \left(T - \frac{1}{4}\right) \]

2. When Amit travels at 60 km/hr, he reaches 15 minutes late. Therefore, the time taken is:
\[ \text{Time} = T + \frac{1}{4} \]
The equation for distance is:
\[ D = 60 \left(T + \frac{1}{4}\right) \]

### Step 3: Set the Two Equations for Distance Equal
Since both expressions for distance \( D \) are equal, we can set them equal to each other:
\[ 80 \left(T - \frac{1}{4}\right) = 60 \left(T + \frac{1}{4}\right) \]

### Step 4: Simplify the Equation
Expanding both sides:
\[ 80T - 20 = 60T + 15 \]
Rearranging gives:
\[ 80T - 60T = 15 + 20 \]
\[ 20T = 35 \]
\[ T = \frac{35}{20} = \frac{7}{4} \text{ hours} = 105 \text{ minutes} \]

### Step 5: Calculate the Distance
Now, substitute \( T \) back into one of the distance equations to find \( D \). Using the first equation:
\[ D = 80 \left(T - \frac{1}{4}\right) = 80 \left(\frac{7}{4} - \frac{1}{4}\right) = 80 \left(\frac{6}{4}\right) = 80 \times \frac{3}{2} = 120 \text{ km} \]

### Step 6: Find the Speed to Reach on Time
To find the speed \( S \) that allows Amit to reach on time, we use the formula:
\[ S = \frac{D}{T} = \frac{120 \text{ km}}{\frac{7}{4} \text{ hours}} = 120 \times \frac{4}{7} = \frac{480}{7} \approx 68.57 \text{ km/hr} \]

### Final Answer
The speed of the car to reach on time is approximately **68.57 km/hr**.