The total value of a collection of coins of denominations Re 1, 50-paise, 25-paise, 10-paise and 5-paise is ₹ 380. If the number of coins of each denomination is the same, then the number of one-rupee coins is

### Concept & Logic Similar to currency note problems, when the quantity of coins for each denomination is identical, we can calculate the value of a single "set" containing one coin of each type, and divide the total sum by this set value. ### Step-by-Step Solution * **Given:** Total value = ₹ 380. Denominations = ₹ 1, 50p, 25p, 10p, 5p. Quantities are equal. * **Calculation:** Let the number of coins for each individual denomination be $x$. * Convert all denominations into Rupees to match the total value unit: * Re 1 = ₹ 1.00 * 50 paise = ₹ 0.50 * 25 paise = ₹ 0.25 * 10 paise = ₹ 0.10 * 5 paise = ₹ 0.05 * Set up the total value equation: $$1.00x + 0.50x + 0.25x + 0.10x + 0.05x = 380$$ * Sum the coefficients: $$1.90x = 380$$ * Solve for $x$: $$x = \frac{380}{1.90} = \frac{3800}{19} = 200$$ * The number of one-rupee coins is exactly $x$, which is 200. ### Exam Strategy & Shortcut Find the value of one coin from every denomination grouped together: $100p + 50p + 25p + 10p + 5p = 190$ paise = ₹ 1.90. Total value is ₹ 380. Divide the total value by the group value: $380 / 1.90 = 200$. This instantly gives you the count for each individual coin type. ### Common Pitfall Miscalculating the sum of the decimal values, particularly messing up $0.10$ and $0.05$, leading to a sum like $1.85$ or $1.95$. Always align decimals carefully when adding denominations. ### Final Answer **Therefore, the correct answer is 200.**