Coin equation (50p and 25p) totaling ₹13.50 A collection of 38 coins consists only of 50 paise and 25 paise coins and totals ₹13.50. How many 25 paise coins are there?

Introduction / Context:This is a linear system with two unknowns: counts of 50p and 25p coins. We use the total count and total value to solve.

Given Data / Assumptions:

• Let x = number of 50p coins; y = number of 25p coins.
• x + y = 38.
• Total value = ₹13.50 = 1350 paise ⇒ 50x + 25y = 1350.

Concept / Approach:Reduce the value equation by 25 to simplify and solve by substitution.

Step-by-Step Solution:From value: 50x + 25y = 1350 ⇒ 2x + y = 54.From count: x + y = 38.Subtract: (2x + y) − (x + y) = 54 − 38 ⇒ x = 16.Then y = 38 − 16 = 22 (25p coins).

Verification / Alternative check:Value = 16×50 + 22×25 = 800 + 550 = 1350 paise = ₹13.50.

Why Other Options Are Wrong:16, 18, 20, 24 do not satisfy both the count and the total value simultaneously.

Common Pitfalls:Mixing rupees and paise; dividing the wrong side by 25 incorrectly.

Final Answer:22