Run until a single potato is out of the bucket

Consider that to take every potato, we need to multiply the distance of the potato by 2 because we need to carry a potato and take it to the bucket. Since the distance between each potato is $1$ meter away and the $1^{\text{st}}$ potato is also $1$ meter away from the bucket, the distance from the nearest to the furthest will form an AP: $1, 2, 3, 4, \dots, 99, 100$

The sum of the AP is: $\begin{aligned} &1+2+3+4+ \cdots +99+100 \\ &= \frac{100(1+100)}{2} \\ &= 50(1+100) \\ &= 50(101) \\ &= 5050 \end{aligned}$

Thus, the total distance that is covered is:

$2 \times 5050 = 10100$

Since the choices are in kilometer, we need to convert the meter into kilometer.

$10100 \text{ m} = 1.01 \text{ km}$

So, the correct answer is $\boxed{10100 \text{ km}}$

For every potato we must multiply by 2 because carrying and putting in the bucket. For 1 potato = 2 m.

Now, coming to AP : 1,2,3,4,5,95,96,97,98,99,100. For finding the sum we use the below formula = n(n+1)/2 = 100(100+1)/2 = 50(101) = 5050.

5050 is for only 50 potatoes For 100 potatoes = 2×5050 = 10100

When shortened , 10.1 km.

@Sandeep Bhardwaj ,isn't this problem like a typical NCERT- level Question? It's still there in class 10th book.

distance covered to collect and store the 1st potato=(1+1)m=2m same for 2nd potato is(2+2)=4m and so on....... so,total distance covered=2(1+2+3+...............100)m=(2) 100 (101)/2=10100m=10.1km