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1.
A container has 80 L of syrup. 8 L is taken out and replaced with water, and this is done three times in all. How much syrup is left?
Correct Answer: B [58.32 L]
Explanation:
80 × (9/10)³ = 80 × 0.729 = 58.32 L.
2.
From a can of 64 L of pure juice, a certain quantity is taken out and replaced with water. This is done once more. The can now has 36 L of juice. How much was taken out each time?
Correct Answer: E [16 L]
Explanation:
(1 − x/64)² = 36/64 → 1 − x/64 = 3/4 → x = 16 L.
3.
60 L of milk and water are in the ratio 2 : 1. How much of the mixture must be taken out and replaced with water so that the ratio becomes 1 : 1?
Correct Answer: D [15 L]
Explanation:
Milk 40 must fall to 30; taking out x removes 2x/3 of milk → 2x/3 = 10 → x = 15 L.
4.
A trader mixes sugar costing ₹ 36 and ₹ 42 per kg and sells the mixture at ₹ 44 per kg, making a profit of 10%. In what ratio did he mix them?
Correct Answer: C [1 : 2]
Explanation:
CP = 44 ÷ 1.1 = 40 → (42 − 40) : (40 − 36) = 2 : 4 = 1 : 2.
5.
Three identical jars are full of milk and water in the ratios 2 : 1, 3 : 2 and 5 : 7. All three are emptied into one large vessel. The ratio of milk to water in it is:
Correct Answer: E [101 : 79]
Explanation:
Milk fractions 2/3, 3/5, 5/12 → average (40 + 36 + 25)/180 = 101/180 → 101 : 79.
6.
Vessel A has milk and water in the ratio 5 : 3 and vessel B in the ratio 2 : 1. How many litres must be taken from A and from B to make 22 L of a mixture with milk : water = 7 : 4?
Correct Answer: A [16 L from A and 6 L from B]
Explanation:
Milk fractions 5/8, 2/3, target 7/11: A : B = (2/3 − 7/11) : (7/11 − 5/8) = 1/33 : 1/88 = 8 : 3 → 16 L and 6 L.
7.
729 L of a mixture has milk and water in the ratio 7 : 2. How much water must be added to make the ratio 7 : 3?
Correct Answer: C [81 L]
Explanation:
Milk 567 = 7 parts → 1 part = 81 → water should be 243; it is 162 → add 81 L.
8.
A jeweller has 24 g of an alloy that is 75% gold. How many grams of pure gold must be added to make it 80% gold?
Correct Answer: D [6 g]
Explanation:
Copper 6 g stays and must be 20% of the new alloy → new weight 30 g → add 6 g of gold.
9.
Tea at ₹ 40 per kg is mixed with a dearer tea in the ratio 5 : 3, and the mixture is worth ₹ 46 per kg. The price of the dearer tea per kg is:
Correct Answer: B [₹ 56]
Explanation:
Cross in reverse: (d − 46) : (46 − 40) = 5 : 3 → d − 46 = 10 → ₹ 56.
10.
A 60 L can holds a 40% sugar solution. How many litres must be taken out and replaced with water so that the solution becomes 30% sugar?
Correct Answer: E [15 L]
Explanation:
0.4 × (1 − x/60) = 0.3 → 1 − x/60 = 3/4 → x = 15 L.
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