Let the fourth proportional be x. 5 : 8 = 15 : x. 5x = 120, so x = 24.

To find the ratio, both quantities must be in the same unit. 1 hour = 60 minutes. The ratio is 25 : 60. Dividing both terms by 5 gives 5 : 12.

Equivalent ratios are obtained by multiplying or dividing both terms of the ratio by the same non-zero number. Multiplying both 5 and 7 by 2 gives 10 : 14.

Given 10% * A = 12% * B, which means 10A = 12B. Therefore, A / B = 12 / 10. Simplifying the fraction gives 6 / 5, so the ratio is 6 : 5.

Let the numbers be 2x and 3x. Sum = 5x = 125, so x = 25. The numbers are 2(25) = 50 and 3(25) = 75.

Let the numbers be 4x and 5x. Their LCM is the product of their unique prime factors, which is 4 * 5 * x = 20x. Given 20x = 180, so x = 9. The smaller number is 4x = 4 * 9 = 36.

To find a : d, multiply all the ratios together: (a/b) * (b/c) * (c/d) = (2/3) * (4/5) * (6/7) = 48 / 105. Simplify by dividing by 3 to get 16 / 35. Ratio is 16 : 35.

Let the shares be 4x and 5x. Given 4x = 200, so x = 50. Total sum = 4x + 5x = 9x. Total = 9 * 50 = Rs. 450.

Let present ages be x and 2x. 5 years back: (x - 5) / (2x - 5) = 1 / 3. Cross-multiplying: 3x - 15 = 2x - 5 => x = 10. Present ages are 10 and 20. After 5 years, ages will be 15 and 25. Ratio is 15 : 25 = 3 : 5.

The ratio of copper to zinc is 5 : 3. Let their weights be 5x and 3x. Given 3x = 24, so x = 8. Total weight is 5x + 3x = 8x. 8 * 8 = 64 grams.