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 meters from the first apple and all other apples are placed 3 meters apart?

Correct Option: (d) 150 m

The competitor starts from the bucket, runs to an apple, and returns to drop it. The first apple is 5 m from the bucket. The distance to collect it and return is 2 × 5 = 10 m. The second apple is 5 + 3 = 8 m from the bucket, so the distance is 2 × 8 = 16 m. Similarly, subsequent apples are placed at increments of 3 m. The distances for the 6 apples are: Apple 1 = 10 m; Apple 2 = 16 m; Apple 3 = 2 × 11 = 22 m; Apple 4 = 2 × 14 = 28 m; Apple 5 = 2 × 17 = 34 m; Apple 6 = 2 × 20 = 40 m. The total distance is the sum of these individual distances: 10 + 16 + 22 + 28 + 34 + 40. This is an arithmetic progression with first term a = 10, common difference d = 6, and number of terms n = 6. The sum is given by (n/2) × (first term + last term) = (6/2) × (10 + 40) = 3 × 50 = 150 m. Hence, option (d) is correct.