Question

The ratio of coins of 1Rs, 50 paise and 25 paise in a bag is $4:5:6$. If the total number of coins is 120 then the number of coins of 25 paise is
 a). 48
 b). 40
 c). 32
 d). None of these

Answer 1

Hint: We can now form an equation using the ratio of coins given and the total number of coins given. We will assume a variable x, then we can write the equation as $4x+5x+6x=120$. Here we have to represent in terms of rupees and not paise, using the relation \[100\text{ }paise\text{ }=\text{ }1\text{ }Rupee\]. After that we will multiply the suitable values to get the total number of 25 paise coins.

Complete step-by-step solution -
It is given in the solution that a bag contains 120 coins in total. Also the type of coins present are also given as 1Re, 50 paise and 25 paise. The ratio of the number of 1 Re, 50 paise and 25 paise coins is given to be \[4:5:6\]. Now we will find the unit value and using unitary method we will try to find the number of 25 paise coins present.
Unitary method is a mathematical approach in which we will first find the value of 1 unit and then multiply accordingly to get the desired value. Let us assume that the number of 1Rs coins = 4x and therefore, according to the question, number of 50 paise coin = $\dfrac{5x}{2}$, similarly number of 25 paise coins = $\dfrac{6x}{4}$ as we know the relation \[100\text{ }paise\text{ }=\text{ }1\text{ }Rupee\]. Or another way is $1Rs=2\times 50paise=4\times 25paise$.
We also know that the sum of these Rs is 120 which can be written as $120\times 100$ paise. Thus we get a relation as $4x+\dfrac{5x}{2}+\dfrac{6x}{4}=120$. Taking LCM of 2,4 as 4 in LHS, we get $\dfrac{16x+10x+6x}{4}=120$, Solving further we get $16x+10x+6x=120\times 4$, therefore calculating the value of x as $32x=480$ or $x=\dfrac{480}{32}=15$.
Thus the number of 1 re coin = $4\times 15=60$, number of 50 paise coins = $5\times 15=75$ and next the number of 25 paise coins = $6\times 15=90coins$. Therefore in the bag, we have 60 coins of Re 1, 75 coins of 50 paise and 90 coins of 25 paise. Hence option d) is correct.

Note: Usually student directly find as $4x+5x+6x=120$ therefore $x=8$ and hence number of 25 paise coins as $6\times 8=48$, which is not correct, because when we take the sum of all the coins it is not equal to Rs.120. Thus, it is necessary to convert all the given values in the same unit before solving.