Question

The number of hours Amaal spends in his game room is proportional to the number of hours he spends playing Call of Destiny IV: Modern Battlefield. If he plays Call of Destiny IV 6 hours, he will spend 8 hours in his game room. How many hours will Amaal spend in his game room if he plays Call of Destiny IV for only 3 hours?
(a) 4
(b) 3
(c) 5
(d) 8

Answer 1

Hint: First, we have to understand what is proportional to what i.e. hours of playing a game is directly proportional to the hours he spends in the game room. Which in mathematical form written as $h\propto g$ where h is for hours in the game room and g is for hours of game played. By using this, we can get our answer.

Complete step-by-step answer:
Here, we are given that the number of hours in the game room is proportional to the hours he plays the game called Call of Destiny IV: Modern Battlefield. This statement can be written in mathematical form as $h\propto g$ where h is for hours in the game room and g is for hours of game played.
So, we are given that if the game is played for 6 hours then Amaal will spend 8 hours in room i.e. $8\propto 6$ . So, we have to find hours in the game room if he plays the game for 3 hours.
${{h}_{1}}\propto {{g}_{1}}\Rightarrow \dfrac{{{h}_{1}}}{{{g}_{1}}}=k$ Here, k is proportionality constant just to remove proportionality sign.
So, we can write equation as
$\dfrac{{{h}_{1}}}{{{g}_{1}}}=\dfrac{{{h}_{2}}}{{{g}_{2}}}$ …………………………….(1)
So, here we will substitute the values i.e. ${{h}_{1}}=8$ , ${{g}_{1}}=6$ , ${{g}_{2}}=3$ in equation (1), we get
$\dfrac{8}{6}=\dfrac{{{h}_{2}}}{3}$
On solving, we get
$\dfrac{8\times 3}{6}={{h}_{2}}$
${{h}_{2}}=4$hours
Thus, 4 hours Amaal will spend in his game room if he plays Call of Destiny IV for only 3 hours.
Hence, option (a) is correct.

Note: Another approach to solve this problem is by unitary method i.e. for playing 6 hours of game, he spends 8 hours in the game room then for 3 hours of game how much time he will spend in the room.
So, using unitary method, we get
$\begin{align}
  & 6\text{ hr of game}=8\text{ hour in room} \\
 & \text{3 hr of game}=? \\
\end{align}$
On simplification, we get
$\dfrac{3\times 8}{6}=4hours$ . So, this is also the approach by which we can get the same answer.