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: Here we go through by supposing the no of coin ratio by multiplying with some variable in their ratio and let it as a number of coins. And then proceed according to the question to find that variable that we suppose. To get the answer.

Given one rupee, 50 paise and 25 paise coins are in the ratio 3:4:5
Now, let the one rupee coins are 3x
And 50 paise coins are 4x
And 25 paise coins are 5x
And now we calculate the value of these coins.
For finding the values of coins first convert their value in one unit .i.e. convert the paise in rupees. And we know that 100 paise is equal to one rupees.
So by applying unitary method we can say that 50 paise= Rs. 0.5 and 25 paise=Rs. 0.25.
Value of one rupee coins $Rs.1 \times 3x = Rs.3x$
Value of 50 paise coin$Rs.0.5 \times 4x = Rs.2x$
Value of 25 paise coin $Rs.0.25 \times 5x = Rs.1.25x$
So we can say that total value of the coin is Rs.3x+Rs.2x+Rs.1.25x=Rs.6.25x
And in the question it is given that the total value of the coin is Rs.93.75.
Now we can equate the value of coins,
i.e. Rs.6.25x=Rs.93.75
$\therefore $x=15
And now we put the value of x that we suppose at the starting of the question. To find the number of coins.
One rupee coins are 3x$ = 3 \times 15 = 45$
50 paise coins are 4x$ = 4 \times 15 = 60$
25 paise coins are 5x$ = 5 \times 15 = 75$
Hence, the required answer is 45, 60, and 75.
So option D is the correct answer.

Note: Whenever we face such types of questions the key concept for solving the question is first always try to assume the given ratio with some variables. Here in this question we will assume the number of coins. After that we need to find the value of coins. Then equate this value with the value that is given in the question. By this process you will find that variable that you let in the number of coins, after putting the value of that variable you will get the answer.