A total of 324 coins of 20 paise and 25 paise make a sum of ₹ 71. The number of 25-paise coins is

### Concept & Logic This is a classic denomination mixture problem that can be solved by setting up simultaneous equations or using a strategic assumption method. We establish an algebraic relationship between the count of the coins and their total monetary value. ### Step-by-Step Solution * **Given:** Total number of coins = 324. Total monetary value = ₹ 71 = 7100 paise. The denominations are 20p and 25p. * **Calculation:** Let the number of 25-paise coins be $x$. * Because there are 324 coins in total, the number of 20-paise coins must be $(324 - x)$. * Set up the total value equation in paise to avoid decimals: $$25x + 20(324 - x) = 7100$$ $$25x + 6480 - 20x = 7100$$ * Isolate $x$: $$5x = 7100 - 6480$$ $$5x = 620$$ $$x = \frac{620}{5} = 124$$ ### Exam Strategy & Shortcut **The "Assume All" Shortcut:** Assume ALL 324 coins were of the lower denomination (20-paise). Total value would logically be $324 \times 20 = 6480$ paise (₹ 64.80). However, the actual value given is 7100 paise (₹ 71.00). The shortfall in our assumption is $7100 - 6480 = 620$ paise. Every time we replace a 20p coin with a 25p coin, the total value increases by 5p. Therefore, the number of 25p coins needed to make up the 620p shortfall is $620 / 5 = 124$. This avoids algebraic equations entirely. ### Common Pitfall Mixing up units between Rupees and Paise. It is always safer and cleaner to convert everything into Paise to avoid decimals during the calculation, which inherently prevents arithmetic errors. ### Final Answer **Therefore, the correct answer is 124.**