Milk water ratio after adding milk – UGC NET Question

Let the original quantities of milk and water be 3x and 2x litres. After adding 10 litres of milk, the quantities become 3x + 10 and 2x, and their ratio is 8:5. Thus, (3x + 10)/(2x) = 8/5. Cross multiplying gives 5(3x + 10) = 16x, so 15x + 50 = 16x and x = 50. The original quantity of milk is therefore 3x = 150 litres.

Option A:
Option A is correct because with x = 50 we have initial milk 150 litres and water 100 litres, giving 3:2. After adding 10 litres of milk, the new quantities are 160 litres of milk and 100 litres of water, giving 160:100 = 8:5, which matches the stated new ratio. This confirms 150 litres as the correct original milk quantity.

Option B:
Option B, 120 litres, would imply x = 40 and water 80 litres initially. Adding 10 litres of milk would give 130 litres of milk and 80 litres of water, yielding a ratio of 130:80 = 13:8, not 8:5. Therefore 120 litres does not satisfy the condition.

Option C:
Option C, 125 litres, does not correspond to a clean multiple of 3 and would make the water quantity non-integral if we tried to preserve the 3:2 ratio. Even if we forced approximate values, the resulting ratio after adding 10 litres of milk would not simplify to 8:5.

Option D:
Option D, 160 litres, would require a smaller water quantity than 100 litres to maintain the initial ratio 3:2. After the addition of milk, the ratio would become even more extreme than 8:5, and a detailed calculation shows it does not fit the given transformation.