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

Introduction / Context:
This is a mixed denomination percentage problem where we work with numbers of coins and their values at the same time. The question checks your ability to convert counts of coins into total money, apply percentage reductions, and then compute the percentage of the total value removed. It is a standard aptitude type question in percentage and simple arithmetic, relevant for banking, insurance, and general competitive exams.

Given Data / Assumptions:

• There are 600 coins of 25 paise denomination.
• There are 1200 coins of 50 paise denomination.
• 12% of the 25 paise coins are removed.
• 24% of the 50 paise coins are removed.
• We are asked to find what percentage of the total money in the bag has been removed.
• We treat 25 paise as 0.25 rupee and 50 paise as 0.50 rupee for calculations.

Concept / Approach:
The key idea is that percentages of coins removed translate to percentages of value removed, but only within each denomination. Because the denominations are different, we must compute the value removed for each type separately and then sum them. First, we calculate the total amount of money in the bag. Next, we find how many coins of each type are removed using the given percentages and convert these removed coins into rupee values. Finally, we compare the total value removed with the original total value and express the result as a percentage. This systematic approach avoids confusion between counts and values.

Step-by-Step Solution:
Step 1: Value of 600 coins of 25 paise = 600 * 0.25 = 150 rupees.Step 2: Value of 1200 coins of 50 paise = 1200 * 0.50 = 600 rupees.Step 3: Total money in the bag initially = 150 + 600 = 750 rupees.Step 4: 12% of 600 coins of 25 paise are removed, that is 0.12 * 600 = 72 coins.Step 5: Value of removed 25 paise coins = 72 * 0.25 = 18 rupees.Step 6: 24% of 1200 coins of 50 paise are removed, that is 0.24 * 1200 = 288 coins.Step 7: Value of removed 50 paise coins = 288 * 0.50 = 144 rupees.Step 8: Total value removed = 18 + 144 = 162 rupees.Step 9: Required percentage removed = (162 / 750) * 100% = 21.6%.

Verification / Alternative check:
An alternative quick check is to compute the percentage of money represented by each denomination and ensure the removal is proportionate. The original total is 750 rupees. The removed amount is 162 rupees. Dividing 162 by 750 gives 0.216. Multiplying this decimal by 100 gives 21.6%. This matches our earlier computation from step-by-step arithmetic. Both methods confirm that the percentage of money removed is 21.6%, and the result is consistent and accurate.

Why Other Options Are Wrong:
Option 15.3% corresponds to a removed amount of approximately 115 rupees, which is less than the actual 162 rupees removed. Option 14.6% would mean about 109.5 rupees removed, again not matching the computed value. Option 12.5% suggests only 93.75 rupees removed, which is clearly too small given the significant removal of 25 paise and 50 paise coins. Option 18.2% represents around 136.5 rupees, still below the correct amount. Since only 21.6% matches 162 out of 750, the other values are incorrect.

Common Pitfalls:
One common error is to take 12% and 24% directly on the total amount without separating the denominations, which leads to wrong values. Another mistake is to convert paise to rupees incorrectly or to treat 25 paise as 25 rupees. Some learners also mistakenly calculate the percentage with respect to the number of coins instead of the total money value. To avoid these errors, always convert counts to values using the correct denomination and only then apply percentages and ratios.

Final Answer:
The percentage of money removed from the bag is approximately 21.6%.