Initial milk = (5/7)*28 = 20 L. Initial water = (2/7)*28 = 8 L. Let x liters of water be added. 20 / (8 + x) = 2 / 5. 100 = 16 + 2x => 2x = 84 => x = 42 liters.

Let numbers be 7x and 11x. (7x + 7) / (11x + 7) = 2 / 3. Cross-multiplying: 21x + 21 = 22x + 14 => x = 7. Smaller number is 7x = 7 * 7 = 49.

Let the number of coins be x, 2x, and 3x. Value in paise: 50x + 25(2x) + 10(3x) = 50x + 50x + 30x = 130x paise. Total amount = 650 paise. 130x = 650 => x = 5. Number of 10 paise coins = 3x = 3 * 5 = 15. Wait, 130x = 650 => x=5. 3x=15. Let me re-read: Option b is 15. Oh, I put option d. Let me correct the correct_option to 'b' for 15.

Difference in ratio parts of C and A is 5 - 2 = 3 parts. 3 parts = 1500, so 1 part = 500. Total parts = 2 + 3 + 5 = 10 parts. Total sum = 10 * 500 = Rs. 5000.

Remaining total = 2430 - (5 + 10 + 15) = 2400. This is divided in ratio 3:4:5. Sum of ratios = 12. B's remainder share = (4/12) * 2400 = 800. B's original share = 800 + 10 = Rs. 810.

The sub-triplicate ratio is the cube root of the given ratio. Cube root of 216 is 6, and cube root of 343 is 7. Thus, 6 : 7.

The triplicate ratio is the cube of the original ratio. 1^3 : 4^3 = 1 : 64.

The sub-duplicate ratio is the square root of the ratio. sqrt(81) : sqrt(64) = 9 : 8.

The duplicate ratio is found by squaring each term of the original ratio. For 4 : 7, it is 4^2 : 7^2 = 16 : 49.

Compounded ratio = (2/3) * (6/11) * (11/2) = (2 * 6 * 11) / (3 * 11 * 2) = 132 / 66 = 2 / 1. The ratio is 2 : 1.