A box contains 1 rupee, 50-paise and 25-paise coins in the ratio 8 : 5 : 3. If the total amount of money in the box is ₹ 112.50, the number of 50-paise coins is

### Concept & Value of Coins To find the total monetary value from a ratio of coins, multiply the number of coins of each denomination by their respective face value in a consistent unit (like Rupees). ### Step-by-Step Solution 1. The ratio of the number of 1 rupee, 50-paise, and 25-paise coins is $8 : 5 : 3$. 2. Let the number of 1 rupee, 50-paise, and 25-paise coins be $8x$, $5x$, and $3x$ respectively. 3. Convert all face values to Rupees to maintain consistency: - 1 rupee = ₹ 1 - 50-paise = ₹ 0.50 - 25-paise = ₹ 0.25 4. Formulate the total value equation: $$ (8x \times 1) + (5x \times 0.50) + (3x \times 0.25) = 112.50 $$ $$ 8x + 2.5x + 0.75x = 112.50 $$ $$ 11.25x = 112.50 $$ 5. Solve for $x$: $$ x = \frac{112.50}{11.25} = 10 $$ 6. The question asks for the number of 50-paise coins, which is represented by $5x$. 7. Number of 50-paise coins = $5(10) = 50$. ### Exam Strategy & Shortcut The number of 50-paise coins is represented by "5" in the given ratio $8:5:3$. Therefore, the correct answer must be a multiple of 5. By quickly testing $x=10$ (which gives 50 coins and makes the math straightforward), we get values of ₹80, ₹25, and ₹7.50. Adding these gives exactly ₹112.50, instantly verifying 50 as the correct option without complex division. ### Common Pitfall Failing to convert the face values of the coins into the same unit (Rupees) before multiplying, or attempting to add the number of coins directly to the total monetary value. ### Final Answer Therefore, the correct answer is **50**.