Question

A bag contains $25$ paise coins, $50$ paise coins and $1$ rupee coins whose values are in the ratio of$8:4:2$. The total values of coins are $840$. Then find the total number of coins.

Answer 1

Hint: A ratio is nothing but the quantitative relation between two numbers that shows how one number is compared with another, and the relation can be between more than two numbers with a condition that their unit must be the same. Generally, we use the symbol”:” to denote a ratio between the numbers.
        In our question, the values of $25$ paise coins, $50$ paise coins, and $1$ rupee coins are in the ratio of $8:4:2$, and the total values of coins are $840$. We are asked to calculate the number of $25$ paise coins, $50$ paise coins, and $1$ rupee coins.

Complete step by step answer:
 It is given that the total values of coins are $840$ .
Let us consider the number of coins $x$.
Also, we are given that values of $25$ paise coins, $50$ paise coins, and $1$ rupee coins are in the ratio of$8:4:2$.
Hence, we get,
\[number{\text{ }}of25paise:number{\text{ }}of50paise:number{\text{ }}of1rupee = 8x:4x:2x\]
Hence, the total number of coins\[ = 8x + 4x + 2x\]
                                                         $ = 14x$
Since it is given that the total values of coins are $840$, we shall compare it with the above value.
That is $840 = 14x$ .
$ \Rightarrow x = \dfrac{{840}}{{14}}$
$ \Rightarrow x = 60$
Since we have \[number{\text{ }}of 25 paise:number{\text{ }}of 50 paise:number{\text{ }}of 1 rupee = 8x:4x:2x\] , we need to substitute the value of $x$.
As the value $25$ paise coins $ = 8x$, we get the number of $25$ paise coins $ = 8 \times 60 \times 4$
                                                                                                                                 $ = 1920$
  (Since $25$ paise is one-fourth of one rupee, we multiplied by $4$ )
As the value $50$ paise coins $ = 4x$, we get the number of $50$ paise coins $ = 4 \times 60 \times 2$
                                                                                                                               $ = 480$
  (Since $50$ paise is one-fourth of one rupee, we multiplied by $2$ )

As the value of $1$ rupee coins $ = 2x$, we get the number of $1$ rupee coins $ = 2 \times 60$
                                                                                                                                  $ = 120$
Therefore, the total number of coins in the bag is \[1920 + 480 + 120 = 2520\]

Note: A ratio is an expression that is used to compare the size of two things or more than two things (i.e.) it is a relationship between more than two numbers with a condition that their units must be the same. Generally, we use the symbol”:” to denote a ratio between the numbers.