Coins in a fixed ratio with a specified total value: A bag contains 25p, 10p, and 5p coins in the ratio 1 : 2 : 3. If the total value is ₹ 60, how many 5p coins are there? (1 rupee = 100 paise.)

Introduction / Context: When coin counts are in a ratio but denomination values differ, total value equals the sum of (count * denomination) across types. Express counts using a common multiplier, compute value per “x”, and solve for x from the total value. Then extract the required count.

Given Data / Assumptions:

• Coin count ratio (25p : 10p : 5p) = 1 : 2 : 3.
• Total value = ₹ 60 = 6000 paise.
• Denominations: 25p, 10p, 5p.

Concept / Approach: Let counts be x, 2x, 3x. Total value V (in paise) = 25x + 10*(2x) + 5*(3x). Simplify, equate to 6000, then solve for x. Finally, 5p coins = 3x.

Step-by-Step Solution:

Verification / Alternative check: Actual value check: 25*100 + 10*200 + 5*300 = 2500 + 2000 + 1500 = 6000 paise = ₹ 60—consistent.

Why Other Options Are Wrong: 200, 180, 240, and 150 do not equal 3x with x = 100; they would produce a total value different from ₹ 60.

Common Pitfalls: Forgetting to convert rupees to paise; mixing value ratio with count ratio; or setting counts directly to 1, 2, 3 instead of x, 2x, 3x.

Final Answer: 300