Not the exact question you were looking for?
Paste your question to our Mathbee AI Mentor below to get an instant step-by-step solution.
Arithmetic Progressions
CBSE 2026 Board Exam Set 3 (Code 30/1/3)
CBSE_BOARD_PYQ_2026_30_1_3
Grade 10
Question:
[Section E - Case Study 2]
In a 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 $10$ potatoes in the line. 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, and runs to the bucket to drop it in, and continues in the same way until all potatoes are in the bucket.
(i) What is the total distance covered to pick up the first potato? [1 Mark]
(ii) What is the distance covered to pick up the second potato? [1 Mark]
(iii) (a) Find the total distance the competitor has to run to pick up all 10 potatoes. [2 Marks]
OR
(iii) (b) Find the distance covered for picking up only the $10^{\text{th}}$ potato. [2 Marks]
In a 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 $10$ potatoes in the line. 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, and runs to the bucket to drop it in, and continues in the same way until all potatoes are in the bucket.
(i) What is the total distance covered to pick up the first potato? [1 Mark]
(ii) What is the distance covered to pick up the second potato? [1 Mark]
(iii) (a) Find the total distance the competitor has to run to pick up all 10 potatoes. [2 Marks]
OR
(iii) (b) Find the distance covered for picking up only the $10^{\text{th}}$ potato. [2 Marks]
Step-by-Step Solution
Key Concept: AP with $a = 10, d = 6, n = 10$. Distance covered for $k$-th potato $= 2(5 + 3(k-1))$.
(i) Distance for 1st potato $= 2 \times 5 = 10$ m. [1.0 Mark]
(ii) Distance for 2nd potato $= 2 \times (5 + 3) = 16$ m. [1.0 Mark]
(iii)(a) AP: $10, 16, 22, \dots$ ($a = 10, d = 6, n = 10$). $S_{10} = \dfrac{10}{2} [2(10) + 9(6)] = 5(20 + 54) = 370$ m. [2.0 Marks]
OR (iii)(b) $a_{10} = a + 9d = 10 + 9(6) = 64$ m. [2.0 Marks]
(ii) Distance for 2nd potato $= 2 \times (5 + 3) = 16$ m. [1.0 Mark]
(iii)(a) AP: $10, 16, 22, \dots$ ($a = 10, d = 6, n = 10$). $S_{10} = \dfrac{10}{2} [2(10) + 9(6)] = 5(20 + 54) = 370$ m. [2.0 Marks]
OR (iii)(b) $a_{10} = a + 9d = 10 + 9(6) = 64$ m. [2.0 Marks]
Correct Answer: (i) 10 m | (ii) 16 m | (iii)(a) 370 m OR (iii)(b) 64 m
Mathbee AI Mentor (Free Demo)
Confused by the solution? Ask the AI to explain a specific step, tell you where you went wrong, or break down the key trap in this question.