Numerical: Mixtures & Alligation MCQ — 15 Practice Questions with Answers

Explanation

Use alligation: cheaper quantity : dearer quantity = (dearer price − mean price) : (mean price − cheaper price). Case 1: water costs ₹0 and milk costs ₹40; water:milk = (40 − 30):(30 − 0) = 10:30 = 1:3, so milk:water = 3:1. Case 2: dearer:cheaper = (48 − 40):(60 − 48) = 8:12 = 2:3. Case 3: cheaper:dearer = (48 − 42):(42 − 36) = 6:6 = 1:1. Therefore, the required sequence is 3:1, 2:3, 1:1.

Explanation

In the original 12-litre mixture, milk : water = 7:5, so milk = 12 × 7/12 = 7 litres and water = 5 litres. After adding 3 litres of water, the milk remains 7 litres, while water becomes 8 litres. The new total quantity is 7 + 8 = 15 litres. Therefore, milk percentage = (7/15) × 100 = 700/15 = 46 2/3%. Thus the assertion is true. The reason gives the same calculation and correctly explains why the assertion is true.

Explanation

Initially the container has 40 litres of pure milk. When 10 litres are removed, the milk left is 40 − 10 = 30 litres. The same 10 litres are then replaced with water, so water in the final mixture is 10 litres. Therefore, milk : water = 30 : 10. Dividing both terms by 10 gives 3 : 1. Hence the final ratio of milk to water is 3 : 1.

Explanation

By alligation, the ratio of the 30% solution to the 50% solution is (50 − 42) : (42 − 30) = 8 : 12 = 2 : 3. So statement 1 is correct and statement 2 is wrong. The total parts are 2 + 3 = 5. The 50% solution contributes 3 parts out of 5, so its share is 3/5 × 100 = 60%. Therefore, statements 1 and 3 are correct.

Explanation

In 32 litres of mixture, milk = 32 × 5/8 = 20 litres and water = 32 × 3/8 = 12 litres. Only water is added, so milk remains 20 litres. Let the added water be x litres. New water quantity = 12 + x. Required ratio is 5:7, so 20 : (12 + x) = 5 : 7. Hence 20 × 7 = 5(12 + x), or 140 = 60 + 5x. Therefore x = 16 litres. So, 16 litres of water must be added.