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Question

Sam's playing a game in which the total score varies directly as the square of the number of coins collected. If he has collected 10 coins, then he gets a score of 500. To reach a high score of 2000 the number of coins he should collect is
  1. 20

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Solution

The correct option is A 20
Let score points of the game be x and number of coins collected be y
Given that xy2
x=k×y2 (let k be a constant)
Given that on collecting 10 coins, the score is 500.
500=k×100k=5
Number of coins that he should collect to get 2000 score points.
2000=5×y2
y2=400y=20
Sam should collect 20 coins to get 2000 score points.

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