Ram travelled 1200km by air which formed `(2)/(5)` of his trip. He travelled one-third of the trip by car and the rest by train. The distance (in km) travelled by train was

Options

A. 480
B. 800
C. 1600
D. 1800

Answer

To solve the problem step by step, let's break it down:

### Step 1: Determine the Total Distance
Let the total distance of Ram's trip be denoted as \( x \).

Given that Ram travelled 1200 km by air, which is \( \frac{2}{5} \) of his total trip, we can set up the equation:
\[ \frac{2}{5} x = 1200 \]

### Step 2: Solve for \( x \)
To find \( x \), we can rearrange the equation:
\[ x = 1200 \times \frac{5}{2} \]
Calculating this gives:
\[ x = 1200 \times 2.5 = 3000 \text{ km} \]

### Step 3: Calculate the Distance Travelled by Car
According to the problem, Ram travelled one-third of the total trip by car. Therefore, the distance travelled by car is:
\[ \text{Distance by car} = \frac{1}{3} \times 3000 = 1000 \text{ km} \]

### Step 4: Calculate the Distance Travelled by Train
Now, we need to find the distance travelled by train. The total distance is 3000 km, and we have already calculated the distances travelled by air and by car:
- Distance by air = 1200 km
- Distance by car = 1000 km

So, the distance travelled by train can be calculated as:
\[ \text{Distance by train} = \text{Total distance} - (\text{Distance by air} + \text{Distance by car}) \]
Substituting the values:
\[ \text{Distance by train} = 3000 - (1200 + 1000) = 3000 - 2200 = 800 \text{ km} \]

### Final Answer
The distance travelled by train is **800 km**.

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