Added acid to change mixture ratio – UGC NET Question

Initially, acid = (3/8) × 40 = 15 litres and water = (5/8) × 40 = 25 litres. Let x litres of acid be added. Then acid becomes 15 + x while water remains 25, and the new ratio is (15 + x):25 = 7:5. Cross-multiplying gives 5(15 + x) = 7 × 25, so 75 + 5x = 175 and 5x = 100, which gives x = 20. Thus, 20 litres of acid must be added.

Option A:
Option A, 12 litres, would make the acid quantity 27 litres while water remains 25 litres, giving a ratio 27:25, which does not simplify to 7:5. It therefore fails to meet the required target ratio and underestimates the amount of acid needed.

Option B:
Option B, 16 litres, leads to acid = 31 litres and water = 25 litres, so the ratio becomes 31:25. This cannot be simplified to 7:5, indicating that 16 litres is still insufficient to reach the desired composition.

Option C:
Option C is correct because it yields acid = 35 litres and water = 25 litres, giving a ratio 35:25, which reduces to 7:5 on dividing both numbers by 5. This matches the requirement exactly and confirms that 20 litres is the correct quantity to add.

Option D:
Option D, 24 litres, would result in acid = 39 litres and water = 25 litres, giving a ratio 39:25. This ratio is more acid-heavy than 7:5 and does not simplify to it, showing that 24 litres of acid overshoots the intended mixture ratio.