Question

In a potato race, a bucket is placed at the starting point, which is $5m$ from the first potato and other potatoes are placed $3m$apart in a straight line.

There are ten potatoes in the line.

The total distance covered in $m$ is$?$

Answer 1

Step 1: Form the arithmetic progression (A.P)

The distance of potatoes from the first bucket is $5m$, the next potato is at $8m$ and similarly they form the following A.P.

A.P$=5,8,11,14,.......$

But, the competitor has to run twice the given distance, in order to bring the potato into the bucket

So, the required A.P is $=10,16,22,28,34,.......$

Step 2: Find the total distance covered

The total distance covered is the sum of all the distances, which is = $S_n=\frac{n}{2}\left[2a+\left(n-1\right)d\right]$

$a=10,d=6,n=10$

$$\begin{gathered} \Rightarrow S_{10}=\frac{10}{2}\left[2\right(10)+(10-1\left)\right(6\left)\right] \\ \Rightarrow S_{10}=5[20+9\times 6] \\ \Rightarrow S_{10}=5[20+54] \\ \Rightarrow S_{10}=5\left[74\right] \\ \Rightarrow S_{10}=370 \end{gathered}$$

Hence, the correct answer is $370m$.