The image contains the following problem written in Hindi:

"5 रु, 2 रु, 1 रु एवं 50 पैसे 2:3:1 अनुपात में कुल 860 रुपये हैं। उन सभी के सिक्कों का अनुपात कितना होगा?"

Translation:

You have a total of ₹860 in the ratio of 5 rupees, 2 rupees, 1 rupee, and 50 paisa coins in the ratio of 2:3:1. What is the total number of coins of each denomination?

Step-by-step solution:

Let's assume that the number of coins for each denomination is in the ratio 2:3:1. Let the number of 5 rupee coins = $2x$, the number of 2 rupee coins = $3x$, the number of 1 rupee coins = $x$, and the number of 50 paise coins = $y$.

Now, convert everything into rupees:

• $5 \, \text{rupee coins contribute}$ = $5 \times 2x = 10x \, \text{rupees}$
• $2 \, \text{rupee coins contribute}$ = $2 \times 3x = 6x \, \text{rupees}$
• $1 \, \text{rupee coins contribute}$ = $x \, \text{rupees}$
• $50 \, \text{paise coins contribute}$ = $\frac{y}{2} \, \text{rupees}$

The total amount of money is given as ₹860, so:

$10x + 6x + x + \frac{y}{2} = 860$

$17x + \frac{y}{2} = 860$

Now, you need another condition to solve for $y$. Usually, it might be in proportion with other coin ratios.

Please confirm if any additional details are provided about $y$. Would you like to go into more detail about this approach or explore similar examples?

Related Questions:

1. What if the ratio of the coins changed to 3:4:2?
2. How would the solution differ if the total amount were ₹1000 instead of ₹860?
3. Can you calculate the total number of coins for different values of $x$?
4. How can you generalize this problem to any number of coins and ratios?
5. What if the problem also included ₹10 coins in the ratio?

Tip:

When dealing with ratio problems involving money, always convert all units to the same (e.g., rupees or paise) for consistent calculations.