A saint has a magic pot. He puts one gold ball of radius 1 mm daily inside it for 10 days. If the weight of the first ball is 1 gm and if the radius of a ball inside the pot doubles every day, how much gold will the saint have gained at the beginning of 10th day?
Explanation:
We know, Weight is directly proportional to Volume which is directly proportional to cube of radius. Hence, if radius of a ball doubles, the volume will become 8 times, hence the weight will also become 8 times.
Ball 1: At the beginning of day 10, the weight of ball 1 would be increased 9 times. ∴ Weight of ball 1 at the beginning of day 10 = 1 × 89.
Ball 2: At the beginning of day 10, the weight of ball 2 would be increased 8 times. ∴ Weight of ball 1 at the beginning of day 10 = 1 × 88.
and so on.
Total weight of all the balls at the beginning of day 10 = 89 + 88 + 87 + ... + 80. = (810 - 1)/(8 - 1) = (230 - 1)/7 gms.
Now, the weight gained = (230 - 1)/7 - 10 = (230 - 71)/7
Hence, option (c).
» Your doubt will be displayed only after approval.
Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.