Practice Questions
Concept Explanation
Mixture problems use ratios of components. If milk : water = 5 : 3, total 8 parts.
When mixing two quantities in ratio a : b, first quantity = Total × a/(a+b).
Replacement and alligation extend this — here focus on ratio of ingredients.
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Q1 EasyMilk and water are mixed in the ratio 4 : 1. In 25 litres of mixture, how much milk is there?ExplanationMilk = 25 × 4/5 = 20 litres.
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Q2 EasySpirit and water are in the ratio 7 : 3. How much spirit is there in 40 litres of mixture?ExplanationSpirit = 40 × 7/10 = 28 litres.
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Q3 EasyAcid and water are mixed in the ratio 2 : 5. In 35 litres, how much acid is present?ExplanationAcid = 35 × 2/7 = 10 litres.
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Q4 EasyTwo liquids are mixed in the ratio 5 : 4 and the total volume is 36 litres. What is the difference between their volumes?ExplanationDifference = 36 × 1/9 = 4 litres.
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Q5 EasyWine and water are mixed in the ratio 3 : 2. How much wine is there in 50 litres of mixture?ExplanationWine = 50 × 3/5 = 30 litres.
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Q6 MediumA mixture contains milk and water in the ratio 5 : 1. On adding 5 litres of water, the ratio of milk to water becomes 5 : 2. The quantity of milk in the mixture is:ExplanationLet milk = 5k and water = k. Then 5k/(k+5) = 5/2 → 2k = k + 5 → k = 5. Milk = 25 litres.
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Q7 MediumIn 64 litres of a mixture, milk and water are in the ratio 5 : 3. How much water is there?ExplanationWater = 64 × 3/8 = 24 litres.
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Q8 MediumCopper and zinc are in the ratio 4 : 3 in an alloy. How much copper is there in 84 kg of alloy?ExplanationCopper = 84 × 4/7 = 48 kg.
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Q9 MediumA mixture has three components in the ratio 3 : 5 : 7 and totals 45 litres. What is the largest component?ExplanationLargest = 45 × 7/15 = 21 litres.
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Q10 MediumBrass has copper and zinc in the ratio 5 : 2. How much zinc is there in 28 kg of brass?ExplanationZinc = 28 × 2/7 = 8 kg.
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Q11 HardIn a mixture of 60 litres, the ratio of milk and water is 2 : 1. If this ratio is to be 1 : 2, then the quantity of water to be further added is:ExplanationMilk = 40 L, water = 20 L. Need milk : water = 1 : 2 → water = 80 L. Water to be added = 60 L.
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Q12 HardTea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be:ExplanationLet third price = x. Then (126 + 135 + 2x)/4 = 153 → 261 + 2x = 612 → x = 175.50.
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Q13 HardIn what ratio must a grocer mix two varieties of tea worth Rs. 60 a kg and Rs. 65 a kg so that by selling the mixture at Rs. 68.20 a kg he may gain 10%?ExplanationCP of mixture = 68.20/1.1 = Rs. 62. By alligation: (65−62):(62−60) = 3:2.
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Q14 HardA can contains a mixture of two liquids A and B in the ratio 7 : 5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7 : 9. How many litres of liquid A was contained by the can initially?ExplanationLet initial quantity = 12x litres. After drawing 9 L, A left = 7x − (7/12)×9 and B left = 5x − (5/12)×9. Adding 9 L of B: A/B = 7/9. Solving gives x = 3, so initial A = 7x = 21 litres.
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DS1 Easy
In a dairy quality check, how much milk is in the mixture?
Statement IMilk and water are in the ratio 5 : 3.
Statement IIThe total mixture is 32 litres.
ExplanationTogether: milk = 32 × 5/8 = 20 litres. -
DS2 Easy
Is the quantity of milk more than the quantity of water?
Statement IMilk : water = 7 : 5.
Statement IIThe total mixture is 60 litres.
ExplanationTogether: milk = 35 L and water = 25 L, so milk is more.
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DS3 Medium
What is the ratio of the two components in the mixture?
Statement IComponent A measures 18 litres.
Statement IIComponent B measures 12 litres.
ExplanationTogether: ratio = 18 : 12 = 3 : 2. -
DS4 Medium
What is the total quantity of the mixture?
Statement IMilk and water are in the ratio 4 : 1.
Statement IIThe quantity of milk is 36 litres.
ExplanationTogether: total = 36 × 5/4 = 45 litres. Both statements are needed.