Introduction / Context:
This question checks understanding of ratio, proportion and handling of mixed denominations in rupees and paise. You are given the total value of coins of three different types and the ratio of their counts. The task is to find the exact number of 50-paise coins, which is a standard type of aptitude problem involving both ratios and basic money calculations.
Given Data / Assumptions:
- Total money in the bag = Rs 51.25.
- Coin types: 2-rupee coins, 50-paise coins and 25-paise coins.
- Ratio of number of coins (2-rupee : 50-paise : 25-paise) = 3 : 5 : 7.
- We assume all coins are of these three denominations only.
Concept / Approach:
Let the common multiplying factor be x. Then the number of 2-rupee coins is 3x, of 50-paise coins is 5x and of 25-paise coins is 7x. We then express the total monetary value in terms of x and equate it to the given total amount. Since 1 rupee = 100 paise, we convert paise to rupees where needed. Solving the resulting linear equation gives x, and then we can find the required number of 50-paise coins which is 5x.
Step-by-Step Solution:
1) Let the number of 2-rupee coins be 3x, 50-paise coins be 5x and 25-paise coins be 7x.
2) Value of 2-rupee coins = 3x * 2 = 6x rupees.
3) Value of 50-paise coins = 5x * 0.5 = 2.5x rupees.
4) Value of 25-paise coins = 7x * 0.25 = 1.75x rupees.
5) Total value = 6x + 2.5x + 1.75x = 10.25x rupees.
6) Given total value is Rs 51.25, so 10.25x = 51.25.
7) Therefore x = 51.25 / 10.25 = 5.
8) Number of 50-paise coins = 5x = 5 * 5 = 25 coins.
Verification / Alternative check:
We can quickly verify by recomputing the total value using x = 5. Number of 2-rupee coins = 15, value = 30 rupees. Number of 50-paise coins = 25, value = 12.5 rupees. Number of 25-paise coins = 35, value = 8.75 rupees. Sum = 30 + 12.5 + 8.75 = 51.25 rupees, which matches the given total amount. Therefore the value of x and thus the number of 50-paise coins is correct.
Why Other Options Are Wrong:
Options A (15) and D (5) are simply smaller multiples of 5 and do not satisfy the total value condition when you recompute. Option B (35) would make the value of 50-paise coins alone too large. Option E (30) also results in a total value different from Rs 51.25. Only 25 coins of 50 paise each fits consistently with both the ratio and the total amount.
Common Pitfalls:
Common mistakes include confusing the ratio of number of coins with the ratio of values, or forgetting to convert paise to rupees correctly. Some learners also mistakenly distribute the total amount directly in the ratio 3 : 5 : 7 as rupees without considering that the denominations are different, which leads to incorrect answers. Always work with the number of coins first, and then convert to value using the denomination of each coin type.
Final Answer:
Thus, the bag contains
25 coins of 50 paise each.
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