Q) In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato. The other potatoes are arranged 3 m apart in a straight line, with a total of 10 potatoes, as shown in the figure:

A competitor starts from the bucket, picks up the nearest potato, runs back to the bucket to drop it in, then returns to pick up the next potato. This process continues until all the potatoes are in the bucket.

Based on the above information, answer the following questions:

(i) What is the distance covered to pick up the first potato and drop it in bucket?  

(ii) What is the distance covered to pick up the second potato and drop it in bucket?

(iii) What is the total distance the competitor has to run?

(iv) If average speed of competitor is 5 m/s, then find the average time taken by competitor to put all the potatoes in the bucket.

[Q 37 – 30/1/3 – CBSE 2026 Question Paper]

Ans:

(i)  Distance covered for first potato:

∵ Distance of first potato from bucket = 5 m

∴ Total Distance covered to & fro = 2 x 5 = 10 m

Therefore total distance covered to pick up first potato & drop in bucket is 10 m.

(ii) Distance covered for first potato:

∵ Distance of second potato from bucket = 8 m

∴ Total Distance covered to & fro = 2 x 8 = 16 m

Therefore total distance covered to pick up second potato & drop in bucket is 16 m.

(iii) total distance covered by competitor:

Step 1: Since each potato is kept uniformly at distance of 3 m, the distances of potatoes from bucket is given by: 5, 8, 11, …..

To complete a step, the competitor has to go to a potato, pick up the potato and come back to bucket to drop the potato in it. Hence, this distance needs to be covered = 2 x distance to potato      [as we have seen in part (i) and (ii) above]

∴ The distances covered to pick each potato & drop in bucket is given by: 10, 16, 22, …..

This gives us an AP, where first term, a = 8 and the common difference, d = 16 10 = 6

Step 2: When competitor will pick up the last potato & drop it in bucket, total distance will be covered.

∴ We need to add all the distances covered to pick up each potato till last one

∴ we need to find sum of this AP till the last term.

∵ Since the sum of first n terms of an AP, S_n = [2 a + (n – 1) d]

Here, n = 10, a = 10, d = 6

∴ Sum of 10 terms, S₁₀ = [2 (10) + (10 – 1) (6)]

∴ S₁₀ = 5 (20 + 9 x 6) = 5 x 74 = 370

Therefore, the total distance covered by the competitor is 370 m

(iv) Average time taken by competitor:

∵ We know that the time taken =

= = 74 seconds

Therefore, the time taken is 74 seconds.

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