Question 441 markVery Short AnswerSection E

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

Arithmetic Progressions
Arithmetic Progressions - Application (Potato Race)

Official answer

16 m — the second potato is 5+3=8 m5 + 3 = 8\text{ m} from the bucket, so the round trip is 8+8=16 m8 + 8 = 16\text{ m}.

Answer keywords:potato racesecond potatoarithmetic progressioncommon differenceround trip distance

Marking scheme

  1. 1.1 mark: correct final answer of 16 m, showing the distance 8 m to the potato doubled for the return trip.

Hint

Second potato is 5+3=8 m5 + 3 = 8\text{ m} from the bucket; double it for the round trip.

Quick oral answer

The second potato is 8 m from the bucket (5 m + 3 m gap), so the round trip is 8+8=16 m8 + 8 = 16\text{ m}.

Common mistakes

  1. 1.Forgetting to add the 3 m gap between the first and second potato before doubling.
  2. 2.Doubling only the gap (3 m) instead of the full distance from the bucket (8 m).

Analysis and explanation

Checks whether the 3 m gap between potatoes is correctly added before doubling for the return trip, revealing the AP's common difference.


Concept

  • Second potato lies 3 m further than the first, so its one-way distance is 5+3=8 m5 + 3 = 8\text{ m}; the round trip doubles this.
  • Comparing 16 m (2nd potato) to 10 m (1st potato) gives common difference d=6 md = 6\text{ m}, since the 3 m gap is doubled on both legs.

Key Points

  • One-way distance to 2nd potato = 8 m; round trip = 16 m.
  • AP so far: 10,16,…10, 16, \ldots with d=6 md = 6\text{ m}.

Common Mistakes

  • Adding the 3 m gap only once instead of accounting for both the outward and return legs.
  • Confusing the one-way gap (3 m) with the round-trip common difference (6 m).

Interesting facts

The pattern of round-trip distances (10,16,22,…10, 16, 22, \ldots) forms an AP with common difference 6 m — exactly twice the 3 m gap between potatoes.

This kind of 'shuttle run' distance problem is also used in physical education research to estimate athlete fatigue over repeated sprints.

Question details

Q44 of 56 questions

Board
CBSE
Class
Class 10
Subject
Mathematics (Standard)
Year
2026
Section
Section E
Marks
1
Type
Very Short Answer
Chapter
Arithmetic Progressions
Topic
Arithmetic Progressions - Application (Potato Race)
Bloom's level
apply
Syllabus topic
Unit II: Algebra — Arithmetic Progressions: real-life application of nth term
Author
CBSE
Reviewed by
Padhantu Academic Team

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Frequently asked questions

What is the common difference of the AP formed here?

6 m, since each potato is 3 m farther than the previous one and the distance is doubled for the round trip (2×3=62 \times 3 = 6).