NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.3 Question 20
NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.3 Question 20
Question:
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 ten 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, 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?
Given:
First potato distance (a) = 5 m
Common difference (d) = 3 m
Number of potatoes (n) = 10
To Find:
Total distance the competitor has to run.
Formula:
Sum of n terms of an AP: Sn = n 2 × [2a + (n − 1)d]
Solution:
The potato are kept at a distance such that it forms an arithmetic progression.
Here,
a = 5,
d = 3,
n = 10
Total distance covered to collect all potato can be found using the sum of n terms of an AP formula: Sn = n 2 × [2a + (n − 1)d]
⇒ Total distance covered to collect all potato = (10/2) × [2 × 5 + (10 − 1) × 3]
⇒ Total distance covered to collect all potato = 5 × [10 + 27]
⇒ Total distance covered to collect all potato = 5 × 37
⇒ Total distance covered to collect all potato = 185
The competitor has to run to the potato collect it and come back the same distance to put it in the bucket.
So, if competitor runs 'D' distance to collect the potato he has to run 'D' distance to put it in the bucket.
So the total distance covered is twice the distance run to take the potato.
⇒ Total distance = 2 × Total distance covered to collect all potato
⇒ Total distance = 2 × S10
⇒ Total distance = 2 × 185
⇒ Total distance = 370 m
Result:
The total distance the competitor has to run is 370 meters.
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