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Class 10 › Mathematics › Arithmetic Progressions
CBSE2026Class Class 10 · Mathematics4 Marks · Long✅ Verified
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. A competitor starts from the bucket, picks up the nearest potato, runs back to drop it in the bucket, then returns for the next potato, and so on until all 10 potatoes are collected. Based on the above information, answer: (i) What is the distance covered to pick up the first potato and drop it in the bucket? [1 mark] (ii) What is the distance covered to pick up the second potato and drop it in the bucket? [1 mark] (iii)(a) What is the total distance the competitor has to run? [2 marks] OR (iii)(b) If the average speed of the competitor is 5 m/s, find the average time taken to put all the potatoes in the bucket. [2 marks]
✅ Answer & Solution
(i) Distance to bucket for 1st potato = 5 m, so round trip = $2\times5=10$ m. (ii) Distance to 2nd potato = $5+3=8$ m, so round trip = $2\times8=16$ m. (iii)(a) The round-trip distances for potatoes 1 to 10 form an AP: $10, 16, 22, ...$ with first term $a=10$ and common difference $d=6$, for $n=10$ terms. Sum $S_{10}=\frac{n}{2}[2a+(n-1)d]=\frac{10}{2}[2(10)+9(6)]=5[20+54]=5\times74=370$ m. So, total distance covered by the competitor $=370$ m. OR (iii)(b) Average time $=\frac{\text{Total distance}}{\text{Average speed}}=\frac{370}{5}=74$ seconds.
