A bag contains 600 coins of 25 p denomination and 1200 coins of 50 p denomination. If 12% of 25 p coins and 24% of 50 p coins are removed, the percentage of money removed from the bag is nearly

### Concept & Logic To find the percentage of money removed, we must calculate the total monetary value initially in the bag and compare it to the total monetary value of the coins that were removed. $$ \text{Percentage Removed} = \left( \frac{\text{Total Value Removed}}{\text{Initial Total Value}} \right) \times 100 $$ ### Step-by-Step Solution * **Given:** * Initial 25 p coins = $600$ * Initial 50 p coins = $1200$ * Removed 25 p coins = $12\%$ * Removed 50 p coins = $24\%$ * **Calculation:** First, find the initial total value in paise: Value of 25 p coins = $600 \times 25 = 15000$ p Value of 50 p coins = $1200 \times 50 = 60000$ p Total Initial Value = $15000 + 60000 = 75000$ p Next, calculate the number of coins removed: Removed 25 p coins = $12\%$ of $600 = \frac{12}{100} \times 600 = 72$ coins Removed 50 p coins = $24\%$ of $1200 = \frac{24}{100} \times 1200 = 288$ coins Now, find the monetary value of the removed coins: Value of removed 25 p coins = $72 \times 25 = 1800$ p Value of removed 50 p coins = $288 \times 50 = 14400$ p Total Value Removed = $1800 + 14400 = 16200$ p Finally, calculate the required percentage: Percentage = $\left( \frac{16200}{75000} \right) \times 100$ Percentage = $\frac{162}{750} \times 100 = \frac{1620}{75} = 21.6\%$ ### Exam Strategy & Shortcut Instead of calculating total massive sums, you can calculate the total value in Rupees to keep numbers smaller: Initial Value = $(600 \times 0.25) + (1200 \times 0.50) = 150 + 600 = 750$ Rupees. Removed Value = $(72 \times 0.25) + (288 \times 0.50) = 18 + 144 = 162$ Rupees. Percentage = $(162 / 750) \times 100 = 21.6\%$. Keeping calculations in a familiar unit (Rupees) prevents arithmetic bloat. ### Common Pitfall A very common mistake is to simply take a weighted average of the *number* of coins removed (i.e., averaging $12\%$ and $24\%$ based on $600$ and $1200$ coins). This gives the percentage of *coins* removed ($20\%$), not the percentage of *monetary value* removed. Always track the denomination multiplier! ### Final Answer Therefore, the correct answer is **21.6%**.