1. Let the number of copper coins be 7x and the number of silver coins be 4x, where x is a common multiplier. 2. The difference between the number of copper coins and silver coins is given as 27. 3. Set up the equation: 7x - 4x = 27. 4. Simplify the equation: 3x = 27. 5. Solve for x: x = 27 / 3 = 9. 6. The total number of coins is the sum of copper and silver coins, which is 7x + 4x = 11x. 7. Substitute the value of x back into the total: Total coins = 11 * 9 = 99. Why others are wrong: A — This represents only the number of copper coins (7 * 9 = 63). B — Correct. C — This error could arise if one correctly finds x=9 but incorrectly assumes the total ratio parts are 12 (e.g., 7+5 instead of 7+4), leading to 9 * 12 = 108. D — This error could arise if one correctly identifies the total ratio parts as 11 but incorrectly assumes the value of x is also 11 (instead of 9), leading to 11 * 11 = 121.

The initial ratio of blue paint to yellow paint is 5:3. This means there are 5 parts of blue paint and 3 parts of yellow paint. The painter adds 4 more parts of yellow paint. The amount of blue paint remains unchanged at 5 parts. The amount of yellow paint becomes 3 (initial parts) + 4 (added parts) = 7 parts. The new ratio of blue paint to yellow paint is therefore 5:7. Why others are wrong: A — This option correctly represents the new ratio after adding yellow paint. B — This option incorrectly assumes the yellow paint quantity changed from 3 parts to 4 parts, rather than increasing by 4 parts. C — This option incorrectly adds 4 parts to the blue paint (5+4=9), or implies a miscalculation for both parts. D — This option incorrectly adds 4 parts to *both* the blue paint (5+4=9) and the yellow paint (3+4=7), which is not stated in the scenario.

1. First, sum the parts of the given ratio: 3 + 5 + 4 = 12 parts. 2. Next, determine the value of one ratio part by dividing the total donation by the total number of parts: $4800 / 12 = $400 per part. 3. Calculate the donation from the Volunteer Association (5 parts): 5 * $400 = $2000. 4. Calculate the donation from the Reading Club (3 parts): 3 * $400 = $1200. 5. Finally, find the difference between their donations: $2000 - $1200 = $800. Why others are wrong: A — This is the calculated value of a single ratio part, not the required difference. C — This is the amount donated by the Reading Club, not the difference asked in the question. D — This is the amount donated by the Volunteer Association, not the difference asked in the question.

1. Identify the given ratios: Gold:Silver = 2:3 and Silver:Bronze = 4:5. 2. Combine the ratios to find a common ratio for Gold:Silver:Bronze. The 'Silver' part is common to both ratios (3 and 4). Find the Least Common Multiple (LCM) of 3 and 4, which is 12. 3. Adjust the first ratio to have 12 for Silver: G:S = (2 * 4) : (3 * 4) = 8:12. 4. Adjust the second ratio to have 12 for Silver: S:B = (4 * 3) : (5 * 3) = 12:15. 5. The combined ratio is G:S:B = 8:12:15. 6. Calculate the total number of parts in the combined ratio: 8 + 12 + 15 = 35 parts. 7. Determine the value of one part: Total medals / Total parts = 105 / 35 = 3 medals per part. 8. Calculate the number of Silver medals: Silver's ratio part * Value per part = 12 * 3 = 36. Why others are wrong: A — This result (21) is obtained by incorrectly summing the initial silver ratio parts (3+4=7) and then calculating (7/35) * 105. B — This result (24) represents the number of Gold medals (8 parts * 3). D — This result (45) represents the number of Bronze medals (15 parts * 3).

The total ratio parts are 3 (for Trust X) + 5 (for Trust Y) = 8 parts. Each ratio part is worth the total amount divided by the total parts: $8400 / 8 = $1050. Trust Y receives 5 parts of the distribution. Therefore, Trust Y receives 5 * $1050 = $5250. Why others are wrong: A — This is the value of one ratio part, not the total amount for Trust Y. B — This is the amount allocated to Trust X (3 * $1050), not Trust Y. C — This would be the amount if the money were split equally, ignoring the given ratio.