Question

Apoorv has only $2$ rupee and $5$ rupee coins in his piggy bank. The total value of the coins is $Rs.132$ . If the number of $2$ rupee coins is $3$ times the number of $5$ rupee coins, find the number of each coin.

Answer 1

Hint: We first let the number of $2$ rupee and $5$ rupee coins be x and y respectively. Then, according to the second statement of the question, we are told that the total value of the coins is $Rs.132$ . This means that,
$\Rightarrow 2x+5y=132....\left( i \right)$
Again, according to the second statement of the question, we are told that the number of $2$ rupee coins is $3$ times the number of $5$ rupee coins. This means that,
$\Rightarrow x=3y....\left( ii \right)$
Solving these two equations gives us the answer.

Complete step by step answer:
In this problem, we are told that Apoorv has only $2$ rupee and $5$ rupee coins in his piggy bank. But nothing is mentioned about their numbers. So, we let the number of $2$ rupee and $5$ rupee coins be x and y respectively.
Now, according to the second statement of the question, we are told that the total value of the coins is $Rs.132$ . This means that,
$\Rightarrow 2x+5y=132....\left( i \right)$
Again, according to the second statement of the question, we are told that the number of $2$ rupee coins is $3$ times the number of $5$ rupee coins. This means that,
$\Rightarrow x=3y....\left( ii \right)$
Using equation (ii) in the first equation, we get,
 $\Rightarrow 2\left( 3y \right)+5y=132$
Solving the above equation, we get,
$\begin{align}
  & \Rightarrow 6y+5y=132 \\
 & \Rightarrow 11y=132 \\
 & \Rightarrow y=12 \\
\end{align}$
Now, from equation (ii), we get,
$\Rightarrow x=3\left( 12 \right)=36$
Thus, we can conclude that the number of $2$ rupee and $5$ rupee coins are $36$ and $12$ respectively.

Note: We can solve this problem by ratios. Now, the number of $2$ rupee coins is three times of $5$ rupee coins. So, their ratio is $3:1$ . The number of $2$ rupee coins will then be $3x$ and the number of $5$ rupee coins will be x. Then,
$\begin{align}
  & \Rightarrow 2\left( 3x \right)+5x=132 \\
 & \Rightarrow x=12 \\
\end{align}$
So, the number of $2$ rupee coins will then be $3x=36$ and the number of $5$ rupee coins will be $x=12$ .