Coin mixture value with ratio counts: A bag contains 25p, 10p, and 5p coins in the ratio 1 : 2 : 3. If the total value is Rs. 30, how many 5p coins are there?

Introduction / Context:
Here the ratio governs counts, not values. You must convert each coin’s count into its rupee value, sum them, equate to the given total, and solve for the common count factor. Finally extract the number of 5p coins from the ratio.

Given Data / Assumptions:

• Counts ratio (25p : 10p : 5p) = 1 : 2 : 3.
• Total value = Rs. 30.
• 1 rupee = 100 paise.

Concept / Approach:
Let counts be x, 2x, 3x. Convert paise to rupees: 25p = 0.25, 10p = 0.10, 5p = 0.05. The total value equation is 0.25x + 0.10(2x) + 0.05(3x) = 30. Solve for x, then compute 3x (the number of 5p coins).

Step-by-Step Solution:
Total value = 0.25x + 0.20x + 0.15x = 0.60x.0.60x = 30 ⇒ x = 50.Number of 5p coins = 3x = 150.

Verification / Alternative check:
Values: 25p coins ⇒ 50 * 0.25 = Rs. 12.50; 10p coins ⇒ 100 * 0.10 = Rs. 10; 5p coins ⇒ 150 * 0.05 = Rs. 7.50; total = Rs. 30.

Why Other Options Are Wrong:

• 50 and 100 correspond to x or 2x, not 3x.
• 200 exceeds the required sum for the given total value.

Common Pitfalls:

• Treating the ratio as values instead of counts.
• Forgetting to convert paise to rupees consistently.

Final Answer:
150