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Q.

In potato race, a bucket is placed at the starting point, which is $5 m$ from the first potato, and the other potatoes are placed $3 m$ apart in a straight line. There are ten potatoes in the line (Fig. given below). 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?

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a

270 m

b

258 m

c

257 m

d

370 m

answer is D.

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Detailed Solution

Given that in a potato race, a bucket is placed at the starting point, the distance between the first potato and the bucket is 5 cm. and also the other potatoes are 3 m placed apart in a straight line. There are 10m potatoes in the line.
We have to find the total distance the competitor has to run.
Question Image

Question Image

By using the sum of the n terms of an AP, we can calculate the distance covered by the competitor first to pick =

2 × 5 = 10 m

Distance covered by the competitor is second to pick: -

2 × (5 + 3 × 1) = 2 × 8 = 16 m

Distance covered by the competitor is third to pick: -

2 × (5 + 3 × 2) = 2 × (5 + 6) = 2 × 11 = 22 m

And so on.
Therefore, the total distance covered by the competitor: -

10, 16, 22, … … u p

to 10 terms.
This is an arithmetic series, Here,

a = 10

,

d = 16 − 10 = 6

and

n = 10

Using the formula: -

S n = n 2 [2 a + (n − 1) d]

Substitute the value in this formula: -

S n = 102 [2 × 10 + (10 − 1) 6] S n = 5 [20 + 54] S n = 5 × 74 S n = 370 m

Thus, the total distance the competitor has to run is 370m.
Therefore, the correct option is 4.

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In potato race, a bucket is placed at the starting point, which is 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 (Fig. given below). 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?