A bag contains an equal number of 1 rupee, 50 paise and 25 paise coins respectively. If the total value is Rs. 35, how many coins of each type are there?

Options

A. 20 coins of each type
B. 21 coins of each type
C. 24 coins of each type
D. 22 coins of each type

Answer

To solve the problem, we need to find out how many coins of each type (1 rupee, 50 paise, and 25 paise) are in the bag, given that they are equal in number and the total value is Rs. 35.

**Step 1: Define the variables.**
Let the number of coins of each type be \( x \).

**Step 2: Calculate the total value of each type of coin.**
- The value of \( x \) coins of 1 rupee is:
\[ 1 \text{ rupee} \times x = x \text{ rupees} \]

- The value of \( x \) coins of 50 paise is:
\[ 50 \text{ paise} = \frac{50}{100} \text{ rupees} = 0.5 \text{ rupees} \]
Therefore, the value of \( x \) coins of 50 paise is:
\[ 0.5 \text{ rupees} \times x = 0.5x \text{ rupees} \]

- The value of \( x \) coins of 25 paise is:
\[ 25 \text{ paise} = \frac{25}{100} \text{ rupees} = 0.25 \text{ rupees} \]
Therefore, the value of \( x \) coins of 25 paise is:
\[ 0.25 \text{ rupees} \times x = 0.25x \text{ rupees} \]

**Step 3: Set up the equation for the total value.**
According to the problem, the total value of all the coins is Rs. 35. Therefore, we can write the equation:
\[ x + 0.5x + 0.25x = 35 \]

**Step 4: Combine like terms.**
Combine the terms on the left side:
\[ x + 0.5x + 0.25x = 1x + 0.5x + 0.25x = 1.75x \]
So the equation becomes:
\[ 1.75x = 35 \]

**Step 5: Solve for \( x \).**
To find \( x \), divide both sides of the equation by 1.75:
\[ x = \frac{35}{1.75} \]
Calculating the right side:
\[ x = 20 \]

**Step 6: Conclusion.**
Thus, the number of coins of each type (1 rupee, 50 paise, and 25 paise) is \( 20 \).

**Final Answer:**
There are 20 coins of each type.

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