Question

A bag contains Rs. 450 in the form of Rs.1 coins , Rs.2coins and 50 paise coins in the ratio 9:7:4. Find the number of coins of each type .

Answer 1

Hint: First we have to assume that each type of coin is a single variable. Then we use the given total to find the number of coins. The sum of all types of coins multiplied their values results in Rs.450. We use this theme in solving this problem.

Complete step-by-step solution:
 Let us consider the single variable as x such that,
Number of Rs.1 coins = 9x
Number of Rs.2 coins =7x
Number of 50 paise coins = 4x
Total amount in bag = Rs.450
The sum of all types of coins multiplied their values results in Rs.450
$ \Rightarrow 9x \times 1 + 7x \times 2 + 4x \times 0.5 = 450 \\
\Rightarrow 9x + 14x + 2x = 450 \\
\Rightarrow 11x + 14x = 450 \\
\Rightarrow 25x = 450 \\
\Rightarrow x = \dfrac{{450}}{{25}} \\
\Rightarrow x = 18 $
Therefore, the value of x =18
Number of Rs.1 coins = 9x = $9 \times 18 = 162$.
Number of Rs.2 coins=7x = $7 \times 18 = 126$.
Number of 50 paise coins =4x= $4 \times 18 = 72$.
Total number of coins = $162 + 126 + 72 = 360$.

Note: The problems like this need the perfect attention while reading the question. All this sort of questions containing ratio are initiated with considering a variable and the process is followed as per the given question and notion of application.