Mixtures and alligation
Ten quantitative aptitude questions, each marked as you answer.
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18 litres of a mixture contains milk and water in the ratio 5 : 4. How much water must be added to make the ratio 2 : 3?
Answer and working
Answer A
Milk = 10 l, water = 8 l. For 2 : 3, water must be 10 × 3/2 = 15 l. Add 15 − 8 = 7 litres.
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In what ratio must rice at ₹45/kg be mixed with rice at ₹72/kg so that the mixture is worth ₹57/kg?
Answer and working
Answer C
By alligation: cheaper : dearer = (72 − 57) : (57 − 45) = 15 : 12 = 5 : 4.
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35 litres of a mixture contains milk and water in the ratio 6 : 1. How much water must be added to make the ratio 3 : 5?
Answer and working
Answer C
Milk = 30 l, water = 5 l. For 3 : 5, water must be 30 × 5/3 = 50 l. Add 50 − 5 = 45 litres.
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In what ratio must rice at ₹43/kg be mixed with rice at ₹79/kg so that the mixture is worth ₹64/kg?
Answer and working
Answer C
By alligation: cheaper : dearer = (79 − 64) : (64 − 43) = 15 : 21 = 5 : 7.
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20 litres of a mixture contains milk and water in the ratio 3 : 2. How much water must be added to make the ratio 3 : 4?
Answer and working
Answer B
Milk = 12 l, water = 8 l. For 3 : 4, water must be 12 × 4/3 = 16 l. Add 16 − 8 = 8 litres.
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In what ratio must rice at ₹26/kg be mixed with rice at ₹66/kg so that the mixture is worth ₹41/kg?
Answer and working
Answer B
By alligation: cheaper : dearer = (66 − 41) : (41 − 26) = 25 : 15 = 5 : 3.
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18 litres of a mixture contains milk and water in the ratio 5 : 1. How much water must be added to make the ratio 3 : 2?
Answer and working
Answer D
Milk = 15 l, water = 3 l. For 3 : 2, water must be 15 × 2/3 = 10 l. Add 10 − 3 = 7 litres.
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36 litres of a mixture contains milk and water in the ratio 5 : 1. How much water must be added to make the ratio 2 : 5?
Answer and working
Answer C
Milk = 30 l, water = 6 l. For 2 : 5, water must be 30 × 5/2 = 75 l. Add 75 − 6 = 69 litres.
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10 litres of a mixture contains milk and water in the ratio 3 : 2. How much water must be added to make the ratio 1 : 2?
Answer and working
Answer D
Milk = 6 l, water = 4 l. For 1 : 2, water must be 6 × 2/1 = 12 l. Add 12 − 4 = 8 litres.
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In what ratio must rice at ₹45/kg be mixed with rice at ₹58/kg so that the mixture is worth ₹54/kg?
Answer and working
Answer A
By alligation: cheaper : dearer = (58 − 54) : (54 − 45) = 4 : 9 = 4 : 9.
More quantitative aptitude: Percentages, Profit, loss and discount, Simple interest, Compound interest, Ratio and proportion, Averages.