Question

A sum of ${{Rs}}6.40$ is made up of 80 coins which are either 10 paise or 5 paise coins. How many coins of 5 paise are there?
A) 28
B) 24
C) 32
D) 36

Answer 1

Hint:
Here, we will assume the number of 10 paise coins to be some variable. Then we will use the given information to find the number of 5 paise coins in terms of the assumed variable. We will simply then multiply the number of coins by their denomination. Then by adding all of them together and equating it to the total sum of money formed in paise will help us to get the value of $x$. Therefore, we will be able to find the required total number of 5 paise coins.

Complete step by step solution:
Let the number of 10 paise coins be $x$.
Now, according to the question, there are a total of 80 coins.
Hence, the number of 5 paise coins will be $\left( {80 - x} \right)$.
Now, the value of 10 paise coins $ = 10x$
And, the value of 5 paise coins $ = 5\left( {80 - x} \right)$
But, the total value of these 80 coins is given as ${\text{Rs}}6.40$.
Now, we know that we have 100 paise in ${\text{Rs}}1$
Hence, in order to convert given amount in rupees to paise, we multiply it by 100
Thus, the total value of the given 80 coins $ = 6.40 \times 100 = \dfrac{{640}}{{100}} \times 100 = 640$ paise
Hence, we will get the mathematical equation as:
$10x + 5\left( {80 - x} \right) = 640$
Multiplying the terms, we get
$ \Rightarrow 10x + 400 - 5x = 640$
Subtracting the like terms, we get
$ \Rightarrow 5x = 640 - 400 = 240$
Dividing both sides by 5, we get
$ \Rightarrow x = 48$
Therefore, the number of 10 paise coins, $x = 48$
Hence, the required number of 5 paise coins, $\left( {80 - x} \right) = \left( {80 - 48} \right) = 32$

Therefore, option C is the correct answer.

Note:
A denomination means the unit value of financial instruments such as coins, currency notes, securities, bonds, etc. While solving the questions related to the denominations of a coin, we must know the difference between the face value and the value of money. This means that if we are given that we have a ${\text{Rs}}2$ coin, then this is the face value of that coin. But, if we are given that we have 20 coins of the denomination ${\text{Rs}}2$. Hence, if we want to know what the value of money with us is then, we would multiply the face value of the denomination by the number of coins of that specific denomination. In this case, the value of money $ = 2 \times 20 = {\text{Rs}}40.