A bag contains ₹1, 50 paise, and 10 paise coins in the ratio 6 : 3 : 2 and the total amount is ₹30.80. How many 50 paise coins are there in the bag?

Introduction / Context:
This question is a standard coins and ratio problem from quantitative aptitude. It tests your ability to translate a ratio into actual numbers, handle mixed denominations, and set up an equation using the total monetary value. Such questions appear frequently in banking, clerical, and management entrance tests.

Given Data / Assumptions:

• The bag contains coins of ₹1, 50 paise, and 10 paise.
• The ratio of their counts is 6 : 3 : 2.
• The total value of all coins together is ₹30.80.
• We need to determine the number of 50 paise coins.

Concept / Approach:
Main ideas:

• Let the common multiplying factor of the ratio be k, so numbers of coins are 6k, 3k, and 2k.
• Convert all coin values to rupees: 50 paise = ₹0.50 and 10 paise = ₹0.10.
• Form an equation for total value and solve for k.
• Use k to find the number of 50 paise coins, which is 3k.

Step-by-Step Solution:
Let the numbers of coins be: ₹1 coins = 6k, 50 paise coins = 3k, 10 paise coins = 2k. Values in rupees: ₹1 coin is 1, 50 paise is 0.5, and 10 paise is 0.1. Total value V = 6k * 1 + 3k * 0.5 + 2k * 0.1. Compute: V = 6k + 1.5k + 0.2k = 7.7k. Given total value is ₹30.80, so 7.7k = 30.80. Solve for k: k = 30.80 / 7.7 = 4. Number of 50 paise coins = 3k = 3 * 4 = 12.

Verification / Alternative check:
Check the total value using k = 4. Numbers of coins: ₹1 coins = 24, 50 paise = 12, 10 paise = 8. Total value = 24 * 1 + 12 * 0.5 + 8 * 0.1 = 24 + 6 + 0.8 = 30.8, that is ₹30.80. This matches the given total, confirming our solution.

Why Other Options Are Wrong:
Option a: 8 would make the total value smaller, and the equation 7.7k = 30.80 would not hold.
Option b: 24 would correspond to k = 8, giving a total much larger than ₹30.80.
Option d: 4 makes k = 4/3, which does not satisfy the original total value condition.
Option e: 16 would give k = 16/3, again not consistent with the total sum.

Common Pitfalls:
Common mistakes include forgetting to convert paise to rupees, treating the ratio numbers as actual counts without using a common factor, and miscalculating the total value. Always maintain consistent units (rupees here) and carefully multiply each coin type by its value and its count before forming the equation.

Final Answer:
The bag contains 12 coins of 50 paise.