To determine a possible distance at which Arun lives from the narrator's place, we need to interpret the given information about the distances of Michael, Ahmed, and Susan, and then apply the conditions provided for Arun's location.

Understanding Given Distances

First, let's list the known distances from where the narrator lives to each person's place:

• Michael's distance: 10 km
• Ahmed's distance: 5 km
• Susan's distance: 7 km

Arun's Distance Range Determination

The problem states two specific conditions regarding Arun's distance:

1. Arun is farther away than Ahmed.
2. Arun is closer than Susan.

Let's use \(D_{Arun}\) to represent the distance of Arun from the narrator's place.

Condition 1: Arun is Farther Away Than Ahmed

Ahmed lives 5 km away. If Arun is farther away than Ahmed, it means Arun's distance must be strictly greater than Ahmed's distance.

Mathematically, this can be written as:

\(D_{Arun} > \text{Ahmed's distance}\)

\(D_{Arun} > 5 \text{ km}\)

Condition 2: Arun is Closer Than Susan

Susan lives 7 km away. If Arun is closer than Susan, it means Arun's distance must be strictly less than Susan's distance.

Mathematically, this can be written as:

\(D_{Arun} < \text{Susan's distance}\)

\(D_{Arun} < 7 \text{ km}\)

Combining Arun's Distance Conditions

By combining both conditions, we can establish a precise range for Arun's distance. Arun's distance must be greater than 5 km AND less than 7 km.

So, the possible range for Arun's distance is:

\(5 \text{ km} < D_{Arun} < 7 \text{ km}\)

This means Arun lives at any distance between 5 km and 7 km, but not exactly 5 km or 7 km.

Checking Given Options for Possible Distance

Now, let's examine the provided options to identify which one falls within the calculated range of \(5 \text{ km} < D_{Arun} < 7 \text{ km}\).

Based on our analysis, only 6.02 km falls within the specified range for Arun's distance. Therefore, 6.02 km is a possible distance at which the narrator lives from Arun's place.