Question

Some one rupee, 50-paise and 25-paise coins make up Rs.93.75 and their numbers are in the proportion of 3:4:5. Find the number of each type of coin.
A.40,70,75
B.46,58,75
C.42,56,70
D.45,60,75

Answer 1

Hint:This problem deals with ratios and proportions. Ratio is a way to compare two quantities by using division. A proportion on the other hand is an equation that says that two ratios are equivalent. If one number in proportion is unknown you can find that number by solving the proportion. So finding the unknown number of coins through the ratio and proportions.

Complete step by step answer:Given that the sum of the given number of all kinds of coins make the amount of Rs.93.75.
We have to find out the number of coins of each type.
As given that these coins are in the proportion of 3:4:5.
Let us assume a variable to each coin as they are different, and equate to the given sum which is Rs.93.75.
The cost of the one rupee is \[x = 1\]
The cost of the 50-paise coin is \[y = 0.5\]
The cost of the 25-paise coin is \[z = 0.25\]
Let the common ratio variable be $p$.
So the sum is given below:
$ \Rightarrow p\left( {3x + 4y + 5z} \right) = 93.75$
Substituting for $x,y$ and $z$, as shown below:
$ \Rightarrow p\left[ {3\left( 1 \right) + 4\left( {0.5} \right) + 5\left( {0.25} \right)} \right] = 93.75$
$ \Rightarrow p\left[ {3 + 2 + 1.25} \right] = 93.75$
Simplifying the above equation, as shown:
$ \Rightarrow p\left[ {6.25} \right] = 93.75$
$\therefore p = 15$
So now calculating the number of coins of each kind is given below:
The number of coins of one rupee are:
$ \Rightarrow 3\left( {15} \right) = 45$
$\therefore $There are 45 coins of one rupee.
The number of coins of 50-paise are:
$ \Rightarrow 4\left( {15} \right) = 60$
$\therefore $There are 60 coins of 50-paise.
The number of coins of 25-paise are:
$ \Rightarrow 5\left( {15} \right) = 75$
$\therefore $There are 75 coins of 25-paise.
Final Answer: The number of each type of coins are 45,60 and 75.

Note:
Please note that while solving the problem, we assumed a common variable of which it denotes the common ratio of the number of coins of each kind, so that the after equating the sum of the total amount, we can find the number of common ratio coins, and multiply it with each of the ratio of number of coins.