Question

The total value of collection of coins of denominations Rs. 1.00, 50 paise, 25 paise, 10 paise, and 5 paise is Rs. 380. If the number of coins of each denomination is the same, then what is the number of one – rupee coins.
(a) 100
(b) 150
(c) 200
(d) 250

Answer 1

Hint: We solve this problem first by converting the paise to rupees by using the result
 \[1\text{ Rupee}=100\text{ paise}\]. After converting paise to rupees we consider the number of each denomination as some variable and use the condition that total amount equals to Rs. 380 to find the value of the variable.

Complete step-by-step answer:
We are given that the denominations of coins are Rs. 1.00, 50 paise, 25 paise, 10 paise, and 5 paise.
We know that
 \[1\text{ Rupee}=100\text{ paise}\]
By using the above equation we can write that
 \[50paise=0.5rupee\]
Similarly by converting the remaining denominations we get
 \[\begin{align}
  & 25paise=0.25rupee \\
 & 10paise=0.1rupee \\
 & 5paise=0.05rupee \\
\end{align}\]
We are given that there are the same numbers of all denominations.
Let us assume that the number of coins of each denomination is \['x'\].

Now, the total amount of \['x'\]coins of each denomination is given as
 \[\begin{align}
  & \Rightarrow T=1\left( x \right)+0.5\left( x \right)+0.25\left( x \right)+0.1\left( x \right)+0.05\left( x \right) \\
 & \Rightarrow T=1.9\left( x \right)....equation(i) \\
\end{align}\]
We are given that the total amount of money as
 \[\Rightarrow T=380.........equation(ii)\]
By combining equation (i) and equation (ii) we get
 \[\begin{align}
  & \Rightarrow 1.9\left( x \right)=380 \\
 & \Rightarrow x=200 \\
\end{align}\]
Since all the denominations are equal in number and equal to \['x'\]we can say that there are 200 numbers of one – rupee coins.

So, the correct answer is “Option C”.

Note: Students will make mistakes in taking the total amount of money. Here, there are denominations of 50 paise, 25 paise, 10 paise, and 5 paise, so first we need to convert them to rupees by using the formula
 \[1\text{ Rupee}=100\text{ paise}\]
But students may miss this point and continue the solution which results in the wrong answer. In any problem we need to apply the conditions and formulas when all the parameters are in the same system of units. This point needs to be taken care of.