Shortcut Trick
Value ratio of ₹1 : 50p : 25p is 3 : 5 : 7.
Convert to coin ratio by multiplying value parts by number of coins per Rupee: 3×1 : 5×2 : 7×4 = 3 : 10 : 28.
Total units = 3 + 10 + 28 = 41 units → 615 coins.
1 unit = 615 ÷ 41 = 15. Number of 50 paise coins = 10 units = 10 × 15 = 150.
∴ The correct answer is 150.
Alternate Method
Given:
Total coins = 615
Value ratio (₹1 : 50p : 25p) = 3 : 5 : 7
Formula Used:
Number of coins = Total Value ÷ Value of one coin
Let the total values of ₹1, 50p, and 25p coins be 3x, 5x, and 7x respectively.
⇒ Number of ₹1 coins = 3x / 1 = 3x
⇒ Number of 50p coins = 5x / 0.5 = 10x
⇒ Number of 25p coins = 7x / 0.25 = 28x
⇒ Total coins = 3x + 10x + 28x = 41x
⇒ 41x = 615
⇒ x = 615 ÷ 41 = 15
⇒ Number of 50 paise coins = 10x = 10 × 15 = 150
∴ The correct answer is 150.
Additional Information
Value to Coin Conversion
To find the number of coins from their total value, multiply the value by the reciprocal of the denomination (e.g., Value of 50p × 2 = Number of 50p coins).
Coin to Value Conversion
To find the value from the number of coins, multiply the count of coins by the value of a single coin (e.g., Number of 25p coins × 1/4 = Total value in ₹).
Ratio Balancing
When solving ratio problems with a total sum given, always ensure all parts of the ratio are in the same units (e.g., convert all denominations to ₹ or all to paise).