In a race, a competitor has to collect 6 apples which are kept in a straight line on a track and a bucket is placed at the beginning of the track which is a starting point. The condition is that the competitor can pick only one apple at a time, run back with it and drop it in the bucket If he has to drop all the apples in the bucket, how much total distance he has to run if the bucket is 5 metres from the first apple and all other apples are placed 3 metres apart ?

The correct option is 150 m.

Let us break down the problem step-by-step to understand how to calculate the total distance run by the competitor.

1. Understanding the Setup:
- The bucket is placed at the starting point (position 0).
- The 1st apple is at a distance of 5 metres from the bucket.
- The remaining 5 apples are placed 3 metres apart from each other along a straight line.

2. Distances of Apples from the Bucket:
Let us calculate the distance of each of the 6 apples from the starting bucket:
- Distance to 1st apple = 5 m
- Distance to 2nd apple = 5 + 3 = 8 m
- Distance to 3rd apple = 8 + 3 = 11 m
- Distance to 4th apple = 11 + 3 = 14 m
- Distance to 5th apple = 14 + 3 = 17 m
- Distance to 6th apple = 17 + 3 = 20 m

3. Calculating the Distance Traveled for Each Apple:
For each apple, the competitor starts at the bucket, runs to the apple, picks it up, and runs back to drop it in the bucket. Therefore, the distance covered for each apple is twice the distance from the bucket to that apple (a round trip).

Let us list the round-trip distance for each apple:
- For 1st apple: 2 × 5 m = 10 m
- For 2nd apple: 2 × 8 m = 16 m
- For 3rd apple: 2 × 11 m = 22 m
- For 4th apple: 2 × 14 m = 28 m
- For 5th apple: 2 × 17 m = 34 m
- For 6th apple: 2 × 20 m = 40 m

4. Total Distance Calculation:
To find the total distance run by the competitor, we sum the round-trip distances for all 6 apples:

$$\text{Total Distance}=10+16+22+28+34+40$$

We can add these numbers directly:
- 10 + 16 = 26
- 26 + 22 = 48
- 48 + 28 = 76
- 76 + 34 = 110
- 110 + 40 = 150

Thus, the total distance the competitor has to run is 150 m.