To solve this problem, let's set up the relationships between the shares of A, B, and C using the information given.

Step 1: Define the variables

• Let $A = x$ rupees.
• Given that for every rupee that A has, C has 5 paise, this means $C = 0.05x$ rupees.
• Let $B = y$ rupees.
• Given that for every rupee that B has, C has 20 paise, this means $C = 0.20y$ rupees.

Step 2: Set up the equations based on the relationships

Since $C$ is related to both $A$ and $B$, we have: $C = 0.05x \quad \text{and} \quad C = 0.20y$

Step 3: Express $y$ in terms of $x$

Since both expressions are equal to $C$, we can equate them: $0.05x = 0.20y$

Now, solve for $y$ in terms of $x$: $y = \frac{0.05x}{0.20} = \frac{x}{4}$

Step 4: Express the total sum

The total sum is given as Rs. 9610: $x + y + C = 9610$

Substitute the expressions for $y$ and $C$: $x + \frac{x}{4} + 0.05x = 9610$

Step 5: Simplify the equation

Combine the terms: $x + 0.25x + 0.05x = 9610$

Add the coefficients: $1.30x = 9610$

Step 6: Solve for $x$

$x = \frac{9610}{1.30} = 7392.31 \, \text{(approx)}$

Step 7: Find C's share

Now that we have $x$, we can find $C$: $C = 0.05x = 0.05 \times 7392.31 = 369.615$

Rounding this to the nearest rupee, C's share is approximately Rs. 370.

Final Answer:

C's share is approximately Rs. 370.

Would you like any details or have any questions? Here are some related questions:

1. How would the solution change if A’s share were given a different ratio to C?
2. What would happen if the total sum was divided equally among A, B, and C?
3. How can the concept of ratios be applied to other real-life situations involving money?
4. What if instead of rupees, the sum was given in dollars with the same ratio?
5. Can you solve a similar problem where the ratio involves a different currency or unit?

Tip: Always check the consistency of units when dealing with ratios, especially when involving different currencies or units of measurement.