A bag contains रु 1, रु 2, and रु 5 coins in the ratio 4:1:2. The total sum of the money in the bag is रु 320. Find the number of coins of each kind.

Answer

To solve the problem, we need to find the number of coins of each kind (रु 1, रु 2, and रु 5) based on the given ratio and total amount. Here’s the step-by-step solution:

### Step 1: Understand the Ratio
The ratio of the number of coins of रु 1, रु 2, and रु 5 is given as 4:1:2. This means:
- Let the number of रु 1 coins be 4x
- Let the number of रु 2 coins be 1x
- Let the number of रु 5 coins be 2x

### Step 2: Calculate the Total Value of Coins
Next, we calculate the total monetary value contributed by each type of coin:
- The value of रु 1 coins = Number of coins × Value per coin = 4x × 1 = 4x
- The value of रु 2 coins = Number of coins × Value per coin = 1x × 2 = 2x
- The value of रु 5 coins = Number of coins × Value per coin = 2x × 5 = 10x

### Step 3: Set Up the Equation
Now, we add up the total values of all the coins and set it equal to the total amount given (रु 320):
\[ 4x + 2x + 10x = 320 \]

### Step 4: Simplify the Equation
Combine like terms:
\[ (4x + 2x + 10x) = 16x \]
So, we have:
\[ 16x = 320 \]

### Step 5: Solve for x
To find the value of x, divide both sides by 16:
\[ x = \frac{320}{16} = 20 \]

### Step 6: Find the Number of Coins
Now that we have the value of x, we can find the number of coins of each type:
- Number of रु 1 coins = 4x = 4 × 20 = 80
- Number of रु 2 coins = 1x = 1 × 20 = 20
- Number of रु 5 coins = 2x = 2 × 20 = 40

### Final Answer
- Number of रु 1 coins = 80
- Number of रु 2 coins = 20
- Number of रु 5 coins = 40