NCERT MATHS CLASS - X
Arithmetic Progressions
Exercise 5.3
Question 20:
In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato and 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?
Sol.
The distances of potatoes are 5, 8, 11, 14 … , which are in A.P.
a = 5, d = 8 − 5 = 3
= 5[10 + 9 × 3]
= 5(10 + 27) = 5(37)
= 185
Since every time she has to run back to the bucket, therefore, the total distance that has to be run by the competitor will be two times of it.
Therefore, total distance that the competitor will run = 2 × 185 = 370 m
Second method :
The distances of potatoes from the bucket are 5, 8, 11, 14…
Distance run by the competitor for collecting these potatoes are two times of the distance at which the potatoes have been kept. Therefore, distances to be run are
10, 16, 22, 28, 34,……….
a = 10
d = 16 − 10 = 6
S10 =?
= 5[20 + 54]
= 5 (74)
= 370
Therefore, the competitor will run a total distance of 370 m.