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Q.

A bucket is set at the starting line, which is 5 meters from the first potato, and the other potatoes are arranged in a straight line, 3 meters apart. Ten potatoes are 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 he continues in the same way until all the potatoes are in the bucket. What should be the total distance the competitor has to run?Question Image


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a

400 m

b

370 m

c

350 m

d

450 m 

answer is B.

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Detailed Solution

Given that a bucket is set at the starting line, which is 5 meters from the first potato, and the other potatoes are arranged in a straight line, 3 meters apart such that there are 10 potatoes in the line.
The distance covered by the competitor to pick and drop the first potato is,
  =2×5 =10 m The distance covered by the competitor to pick and drop the second potato is,
=2×(5+3) =2×8 =16 m The distance covered by the competitor to pick and drop the third potato is,
=2×(5+3+3) =2×11 =22 m
So, total distance covered by the competitor =10 m+16 m+22 m+ upto 10 terms  .
The above series is an arithmetic series.
a=10 and n=10 d=1610 d=6
Formula used for sum of first n term of A.P.:
S n = n 2 [2a+(n1)d]
Applying sum of n terms of an A.P. formula:
S 10 = 10 2 [2×10+(101)×6] S 10 =5×(20+54) =5×74 =370   Therefore, the total distance the competitor has to run is 370 m.
Hence, option (2) is correct.
 
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