# Q : 20   In a potato race, a bucket is placed at the starting point, which is $\small 5$ m from the first potato, and the other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line (see Fig. $\small 5.6$).            A competitor starts from the bucket, picks up the nearest potato, runs back with it,  drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What  is the total distance the competitor has to run?             [Hint : To pick up the first potato and the second potato, the total distance (in metres) run by a competitor is  $\small 2\times5+2\times (5+3)$  ]

G Gautam harsolia

Distance travelled by the competitor in picking and dropping 1st potato $= 2 \times 5 = 10 \ m$

Distance travelled by the competitor in picking and dropping 2nd potato $= 2 \times (5+3) =2\times 8 = 16 \ m$

Distance travelled by the competitor in picking and dropping 3rd potato $= 2 \times (5+3+3) =2\times 11 = 22 \ m$

and so on
we can clearly see that it is an AP with first term (a) = 10  and common difference(d) = 6
There are 10 potatoes in the line
Therefore, total distance travelled by the competitor in picking and dropping  potatoes is
$S_{10}= \frac{10}{2}\left \{ 2\times 10+(10-1)6 \right \}$
$S_{10}= 5\left ( 20+54 \right )$
$S_{10}= 5\times 74 = 370$

Therefore, total distance travelled by the competitor in picking and dropping  potatoes is  370 m

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