Question

In a potato race,$20$ potatoes are placed in a line at intervals of $4\mathrm{meters}$ with the first potato$24\mathrm{meters}$ from the starting point. A contestant is required to bring the potatoes back to the starting place one at a time. How far would he run in bringing back all the potatoes?

• A. $2340$
• B. $2480$
• C. $2540$
• D. $2230$

Answer 1

The correct option is B

$2480$

Explanation of correct answer

Finding the distance to bring back all the potatoes:

Total number of potatoes $=20$

The first potato from the starting point is at a distance $=24\mathrm{meters}$

The length of the intervals afterwards $=4\mathrm{meters}$

If the first potato is $24\mathrm{meters}$ from starting line then, the distance he has to travel to bring back the potato is $48\mathrm{metres},$ , now he will travel $24+4=28\mathrm{meters}$ to pick the second potato so the total distance covered to bring back the second potato is $56\mathrm{meters}$, it will go on like this and form the following AP.

A.P. = $48,56,64\dots \dots \dots .{20}^{th}$ terms

Here,

$$\begin{gathered} a=48 \\ d=8 \\ n=20 \end{gathered}$$

Sum of n terms in A.P.,

$\Rightarrow S_n=\frac{n}{2}[2a+(n–1\left)d\right]$

$\Rightarrow S_{20}=\frac{20}{2}[2x48+(20–1\left)8\right]$

$\Rightarrow S_{20}=\frac{20}{2}[96+152]$

$\Rightarrow S_{20}=10\left[248\right]$

$\Rightarrow S_{20}=2480$

Hence, the correct option is $\left(\mathrm{B}\right)2480\mathrm{meters}$.