Half way through the journey from Delhi to Lahore Atalji began to look out of the window of the Samjhauta Express and continued it unit the distance which was remained to cover was half of what he has covered. Now at this time how much distance he has to cover?

Options

A. `2/2`
B. `1/4`
C. `1/3`
D. `1/6`

Answer

To solve the problem step by step, let's break down the journey from Delhi to Lahore and find out how much distance Atalji has to cover when he looks out of the window.

### Step 1: Understand the Total Distance
Let's assume the total distance from Delhi to Lahore is represented as \( D \).

### Step 2: Determine Halfway Point
Halfway through the journey means Atalji has covered half of the total distance. Therefore, the distance covered at this point is:
\[ \text{Distance Covered} = \frac{D}{2} \]

### Step 3: Remaining Distance
At this halfway point, the remaining distance to cover is also:
\[ \text{Remaining Distance} = D - \frac{D}{2} = \frac{D}{2} \]

### Step 4: Atalji's Observation
Atalji continues to look out of the window until the distance remaining to cover is half of what he has already covered. Since he has already covered \( \frac{D}{2} \), half of that distance is:
\[ \text{Half of Covered Distance} = \frac{1}{2} \times \frac{D}{2} = \frac{D}{4} \]

### Step 5: Calculate Remaining Distance When He Looks Out
At this point, the remaining distance to cover will be:
\[ \text{Remaining Distance} = \frac{D}{2} - \frac{D}{4} = \frac{D}{4} \]

### Conclusion
Thus, when Atalji looks out of the window, the distance he has left to cover is:
\[ \frac{D}{4} \]

### Final Answer
So, the distance Atalji has to cover at that time is \( \frac{D}{4} \).

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