A rail journey of 75 km costs ₹ 215. How much will a journey of 120 km cost?

Options

A. ₹344
B. ₹ 324
C. ₹268.75
D. none of these

Answer

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

### Step 1: Determine the cost per kilometer
We know that a journey of 75 km costs ₹ 215. To find the cost for 1 km, we divide the total cost by the distance.

\[ \text{Cost per km} = \frac{\text{Total Cost}}{\text{Distance}} = \frac{215}{75} \]

### Step 2: Simplify the fraction
Now, we can simplify the fraction \(\frac{215}{75}\).

\[ \frac{215}{75} = \frac{43}{15} \text{ (after dividing both the numerator and denominator by 5)} \]

### Step 3: Calculate the cost for 120 km
Now that we have the cost per kilometer, we can find the cost for 120 km by multiplying the cost per km by 120.

\[ \text{Cost for 120 km} = \text{Cost per km} \times 120 = \frac{43}{15} \times 120 \]

### Step 4: Simplify the multiplication
To simplify this calculation, we can first divide 120 by 15.

\[ 120 \div 15 = 8 \]

Then, we multiply the result by 43.

\[ \text{Cost for 120 km} = 43 \times 8 = 344 \]

### Final Answer
Thus, the cost of a journey of 120 km is ₹ 344.

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