Mixed coins, fixed total value: A bag contains ₹1, 50 paise, and 25 paise coins in the ratio 8 : 9 : 11. If the total money is ₹ 366, find how many 25 paise coins are in the bag. Use paise to avoid decimal confusion.

Introduction / Context: When coin counts are in a ratio but denominations differ, compute total value in a single unit (paise) and express counts as multiples of a common variable. This yields a single linear equation in that variable.

Given Data / Assumptions:

• Denominations: ₹1 = 100p, 50p, and 25p.
• Count ratio = 8 : 9 : 11.
• Total value = ₹ 366 = 36,600 paise.

Concept / Approach: Let counts be 8x, 9x, and 11x. Total value V = 100*(8x) + 50*(9x) + 25*(11x). Set V = 36,600 and solve for x to get the 25p coin count = 11x.

Step-by-Step Solution:

Verification / Alternative check: Value check: 100*192 + 50*216 + 25*264 = 19,200 + 10,800 + 6,600 = 36,600 paise = ₹ 366.

Why Other Options Are Wrong: 364, 241, 245, 220 would produce incorrect totals and violate the 8 : 9 : 11 count ratio when verified.

Common Pitfalls: Mixing number ratio with value ratio or forgetting to convert rupees to paise before forming the equation.

Final Answer: 264