Question

In a potato race $20$ potatoes are placed in a line at intervals of $4$ metres with the first potato $24$ metres 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. $2340$ m
• B. $2480$ m
• C. $2540$ m
• D. $2230$ m

Answer 1

The correct option is B $2480$ m

Given, total number of potatoes = 20.

First potato 24 metres from the starting point.

There are 4 meters in the intervals.

A contestant is required to bring the potatoes back to the starting place one at a time.

So for the first potato he has to travel 48 meters, for second 56 meters ...

48,56,64...........20 terms.

a = 48, d= 8, n = 20.

Sum of n terms in A.P $=S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

$S_{20}=\frac{20}{2}[2\times 48+(20-1\left)8\right]$

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

$S_{20}=10\times 248=2480$

$\therefore 2480$ meters he run in bringing back all the potatoes.