Question

A man has only 20 paisa coins and 25 paisa coins in his purse. If he has 50 coins in all totalling Rs. 11.25, how many coins of each kind does he have?

Answer 1

Hint: We solve this problem by assuming the number of coins of each denomination as some variables.
Then we get one equation from the condition that he has a total of 50 coins.
Then we get another equation from the condition that total money equal to Rs. 11.25.
We use the conversion of rupees to paisa as
\[1rupee=100paisa\]

Complete step by step answer:
We are given that a person has only 20 paisa coins and 25 paisa coins in his purse
Let us assume that the number of 20 paisa coins and 25 paisa coins in his purse as \[x,y\] respectively.
We are given that he has a total of 50 coins in his purse.
By converting the above statement into mathematical equation we get
\[\begin{align}
  & \Rightarrow x+y=50 \\
 & \Rightarrow y=50-x.......equation(i) \\
\end{align}\]
We are also given that the person has total of Rs. 11.25 in his purse.
Let us convert the given amount of rupees to paisa.
We know that the conversion of rupees to paisa as
\[1rupee=100paisa\]
By using the above conversion we get the value of Rs. 11.25 in paisa as
\[\begin{align}
  & \Rightarrow Rs11.25=\left( 11.25\times 100 \right)paisa \\
 & \Rightarrow Rs11.25=1125paisa \\
\end{align}\]
We know that if there are \[x\] coins of 20 paise then the total amount will be \[20x\]
Similarly, if there are \[y\] coins of 25 paise then the total amount will be \[25y\]
We are also given that the person has a total of 1125 paisa in his purse.
Now, by converting the above statement into mathematical equation we get
\[\Rightarrow 20x+25y=1125\]
Now, by substituting the value of \[y\] in terms of \[x\] from equation (i) in above equation we get
\[\begin{align}
  & \Rightarrow 20x+25\left( 50-x \right)=1125 \\
 & \Rightarrow 20x+1250-25x=1125 \\
 & \Rightarrow 5x=1250-1125 \\
 & \Rightarrow x=\dfrac{125}{5}=25 \\
\end{align}\]
Now, by substituting the value \[x=25\] in equation (i) we get
\[\begin{align}
  & \Rightarrow y=50-25 \\
 & \Rightarrow y=25 \\
\end{align}\]
Therefore we can conclude that the number of 20 paisa coins is 25 and the number of 25 paisa coins is 25.

Note:
Students may do a mistake that is taking the equation of amount without conversion.
We are given that the person has a total of Rs. 11.25 in his purse.
By converting the above statement into a mathematical equation we get
\[\Rightarrow 20x+25y=11.25\]
This gives the wrong answer because the unit in the LHS is paisa whereas the unit in RHS is rupees.
We know that we can add or subtract or multiply or divide only the terms with the same units.
So, we need to convert the given amount from rupee to paisa or paisa to rupee to get the correct answer.