QUESTION

CSAT

Hard

Reasoning

Prelims 2016

In a race, a competitor has to collect 6 apples which are kept in a straight line on a track and a bucket is placed at the beginning of the track which is a starting point. The condition is that the competitor can pick only one apple at a time, run back with it and drop it in the bucket. If he has to drop all the apples in the bucket, how much total distance he has to run if the bucket is $5$ meters from the first apple and all other apples are placed $3$ meters apart?

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Explanation

Given: Distance from the bucket to the first apple = 5 meters Distance between consecutive apples = 3 meters Number of apples to collect = 6

Step-by-Step Calculation: Distances to collect each apple and return:

For the 1st apple: Distance = $5$ meters (to the apple) + $5$ meters (back) = $10$ meters
For the 2nd apple: Distance = $(5 + 3)$ meters = $8$ meters (to the apple) + $8$ meters (back) = $16$ meters
For the 3rd apple: Distance = $(5 + 3 \times 2)$ meters = $11$ meters (to the apple) + $11$ meters (back) = $22$ meters
For the 4th apple: Distance = $(5 + 3 \times 3)$ meters = $14$ meters (to the apple) + $14$ meters (back) = $28$ meters
For the 5th apple: Distance = $(5 + 3 \times 4)$ meters = $17$ meters (to the apple) + $17$ meters (back) = $34$ meters
For the 6th apple: Distance = $(5 + 3 \times 5)$ meters = $20$ meters (to the apple) + $20$ meters (back) = $40$ meters