Ram arrives at a Bank 15 minutes earlier than scheduled time If he drives his car at 42km/hr. If he drives car at 35km/hr he arrives 5 minutes late. The distance of the Bank from his starting point is

Options

A. 70km
B. 210km
C. 72km
D. 60km

Answer

To solve the problem, we will use the information provided about Ram's travel times at two different speeds.

### Step-by-Step Solution:

1. **Define the Variables:**
Let the distance from Ram's starting point to the bank be \( D \) kilometers.
Let the scheduled time to reach the bank be \( T \) hours.

2. **Calculate Time Taken at Different Speeds:**
- When Ram drives at 42 km/hr, he arrives 15 minutes early. Therefore, the time taken is:
\[ \text{Time at 42 km/hr} = T - \frac{15}{60} = T - \frac{1}{4} \text{ hours} \]
Using the formula \( \text{Distance} = \text{Speed} \times \text{Time} \):
\[ D = 42 \left(T - \frac{1}{4}\right) \]

- When Ram drives at 35 km/hr, he arrives 5 minutes late. Therefore, the time taken is:
\[ \text{Time at 35 km/hr} = T + \frac{5}{60} = T + \frac{1}{12} \text{ hours} \]
Again using the distance formula:
\[ D = 35 \left(T + \frac{1}{12}\right) \]

3. **Set Up the Equations:**
Since both expressions equal \( D \), we can set them equal to each other:
\[ 42 \left(T - \frac{1}{4}\right) = 35 \left(T + \frac{1}{12}\right) \]

4. **Expand and Simplify the Equation:**
Expanding both sides:
\[ 42T - 10.5 = 35T + \frac{35}{12} \]
Rearranging gives:
\[ 42T - 35T = 10.5 + \frac{35}{12} \]
Simplifying the left side:
\[ 7T = 10.5 + \frac{35}{12} \]

5. **Convert 10.5 to a Fraction:**
Convert 10.5 to a fraction:
\[ 10.5 = \frac{21}{2} \]
Now find a common denominator to add:
\[ \frac{21}{2} = \frac{126}{12} \]
So,
\[ 7T = \frac{126}{12} + \frac{35}{12} = \frac{161}{12} \]

6. **Solve for \( T \):**
\[ T = \frac{161}{12 \times 7} = \frac{161}{84} \text{ hours} \]

7. **Calculate the Distance \( D \):**
Now substitute \( T \) back into one of the distance equations. Using \( D = 42 \left(T - \frac{1}{4}\right) \):
\[ D = 42 \left(\frac{161}{84} - \frac{21}{84}\right) = 42 \left(\frac{140}{84}\right) = 42 \times \frac{20}{12} = 70 \text{ km} \]

### Final Answer:
The distance of the bank from Ram's starting point is **70 km**.