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

• A. 20

Answer 1

The correct option is A 20
Let score points of the game be $x$ and number of coins collected be $y$
Given that $x\propto y^2$
$\Rightarrow x=k\times y^2$ (let $k$ be a constant)
Given that on collecting 10 coins, the score is 500.
$\Rightarrow 500=k\times 100\Rightarrow k=5$
Number of coins that he should collect to get $2000$ score points.
$\Rightarrow 2000=5\times y^2$
$\Rightarrow y^2=400\Rightarrow y=20$
$\therefore$ Sam should collect 20 coins to get 2000 score points.