Question

In a video game, each player starts the game with k points and loses 2 points each time a task is not completed. If a player who gains no additional points and fails to complete 100 tasks has a score of 200 points, what is the value of k?
a)0
b)150
c)250
d)400

Answer 1

Hint: In this question, we have to find the initial number of points k which is given to the player. As 2 points are lost by the player every time he fails to complete a task and it is given that the player gained no additional points, the final number of points should be equal to $ k-2\times 100 $ . It is given that the final number of points is 200, therefore we can equate $ k-2\times 100 $ to 200 and solve the equation to find the value of k.

Complete step-by-step answer:
In this question, we are given that the initial number of points of the player=k…………………………..(1.1)
As the player failed to complete 100 tasks and 2 points are lost by the player every time he fails to complete a task,
Total number of points lost by the player= $ 2\times 100 $ ………………………….(1.2)
As the player has gained no additional points, then from (1.1) and (1.2), we obtain
Final score of the player= Initial score-Points lost= $ k-2\times 100 $ ……………………………(1.3)
As it is given that the final score of the player is 200, therefore from (1.3), we should have
  $ \begin{align}
  & k-2\times 100=200 \\
 & \Rightarrow k=200+2\times 100=200+200=400 \\
\end{align} $
Which matches option (d). Thus, option (d) is the correct answer to this question.

Note: We should note that if the player would have gained any additional points, say m, then in equation (1.3), we should have had the final score as \[k-2\times 100+m\] . However, as it is given that the player has gained no additional points, m=0 and thus equation (1.3) in the solution is valid.