A bag contains Rs. 43 in the form of 5-rupee coins, 50-paise coins and 10-paise coins in the ratio 1 : 5 : 11 respectively. What is the total number of 50-paise coins in the bag?

Introduction / Context:
This is a coin and ratio problem involving different denominations with a known total value. The numbers of 5-rupee, 50-paise and 10-paise coins are in a certain ratio. The total amount of money in the bag is given, and we must find how many 50-paise coins are present. This tests the ability to convert coin counts to rupee values and solve a simple linear equation based on ratios.

Given Data / Assumptions:

• Denominations: Rs. 5, Rs. 0.50 (50 paise), Rs. 0.10 (10 paise).
• Counts are in the ratio 1 : 5 : 11 respectively.
• Total money in the bag = Rs. 43.
• We must find the number of 50-paise coins.

Concept / Approach:
We represent the numbers of 5-rupee, 50-paise and 10-paise coins as k, 5k and 11k respectively, using the given ratio. We then write an equation for the total value in rupees by multiplying each coin count by its denomination and summing. This total must equal Rs. 43. Solving for k gives the exact counts of each coin type. The number of 50-paise coins is simply 5k.

Step-by-Step Solution:

Verification / Alternative check:
Check all coin counts and total. With k = 5, 5-rupee coins = 5, 50-paise coins = 25, 10-paise coins = 55. Compute total value: 5 * 5 = Rs. 25; 25 coins of 0.50 each = Rs. 12.5; 55 coins of 0.10 each = Rs. 5.5. Sum = 25 + 12.5 + 5.5 = Rs. 43, which matches the given total. Therefore, the answer is consistent.

Why Other Options Are Wrong:

• 5, 55 and 50 would correspond to different values of k and would not lead to a total of Rs. 43 when combined with the corresponding numbers of 5-rupee and 10-paise coins.
• For example, if there were 50 coins of 50-paise, the value from them alone would be Rs. 25, and it would be difficult to adjust other coins to keep the ratio and still total Rs. 43.

Common Pitfalls:
One common mistake is to confuse the value ratio with the count ratio and directly assign rupee values like 1, 5, 11 rupees. Another is mishandling decimal calculations for 0.50 and 0.10, leading to an incorrect equation. Carefully converting each type of coin to rupees and summing is essential.

Final Answer:
The bag contains 25 coins of 50 paise.