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Mixture and alligation practice questions for bank exams

By the PrepMatic team · Updated 9 Oct 2026 · 4 min read

A mixture question blends two or more ingredients of different price, strength or concentration and asks for the ratio, the quantity or the final value. Alligation is the shortcut that finds the mixing ratio from three numbers, without forming equations. Bank exams use both in short problems on rice, milk, alloys and solutions. The five questions below cover the main types.

The alligation rule

Place the cheaper (or weaker) value on the left, the dearer (or stronger) value on the right, and the mean value in the middle. The quantities are in the ratio of the distances taken crosswise.

The rule works for prices, percentages of alcohol or sugar, and the interest rates in a split investment.

Five practice questions

Question 1

In what ratio should rice costing ₹40 per kg be mixed with rice costing ₹55 per kg so that the mixture is worth ₹48 per kg? Give the ratio as cheaper rice : dearer rice.

• A. 7 : 8
• B. 8 : 7
• C. 3 : 5
• D. 5 : 3

Question 2

A 60-litre mixture of milk and water contains milk and water in the ratio 2 : 1. How much water must be added to make the ratio 1 : 1?

• A. 10 litres
• B. 15 litres
• C. 20 litres
• D. 30 litres

Question 3

A vessel holds 40 litres of pure milk. Four litres are removed and replaced with water. The same step is repeated once more. How much milk is in the vessel now?

• A. 32 litres
• B. 32.4 litres
• C. 33.6 litres
• D. 36 litres

Question 4

Two alloys contain copper and zinc in the ratios 5 : 3 and 1 : 3. In what ratio, first alloy to second alloy, must they be melted together to get an alloy with copper and zinc in the ratio 1 : 1?

• A. 1 : 2
• B. 1 : 1
• C. 3 : 2
• D. 2 : 1

Question 5

How many litres of an 80% alcohol solution must be added to 30 litres of a 20% alcohol solution to get a 40% solution?

• A. 10 litres
• B. 15 litres
• C. 20 litres
• D. 45 litres

Answers and explanations

1. A. Cheaper : dearer = (55 − 48) : (48 − 40) = 7 : 8. Check: 7 kg at ₹40 plus 8 kg at ₹55 costs 280 + 440 = 720 for 15 kg, which is ₹48 a kg. The reverse ratio 8 : 7 is the trap.
2. C. Milk is 40 litres and water is 20 litres. Keep milk fixed and make water equal to it: 40 litres of water, so 20 litres must be added.
3. B. Each step keeps 90% of the milk, because 4 of 40 litres are removed. So 40 × 0.9 × 0.9 = 32.4 litres. The linear guess of 32 litres ignores that the second removal takes out some water.
4. D. The copper fraction is 5/8 in the first alloy and 1/4 in the second, and the target is 1/2. The first : second ratio is (1/2 − 1/4) : (5/8 − 1/2) = 1/4 : 1/8 = 2 : 1. Check: 2 units of the first and 1 of the second give copper 10/8 + 2/8 = 12/8 and zinc 6/8 + 6/8 = 12/8, which is 1 : 1.
5. B. By alligation, 80% solution : 20% solution = (40 − 20) : (80 − 40) = 20 : 40 = 1 : 2. With 30 litres of the 20% solution, the 80% solution needed is 15 litres. Check: 12 + 6 = 18 litres of alcohol in 45 litres, which is 40%.

How to prepare mixtures and alligation

• Draw the cross every time. Writing the three values and the two differences avoids mixing up which side gets which number.
• Convert ratios into fractions. For alloys (Question 4), turn "5 : 3" into "5/8 copper" so that the values are comparable single numbers.
• Use the replacement formula for repeated removal. Each step multiplies the milk by (1 − removed ÷ total).
• Fix one ingredient. In dilution problems (Question 2), the quantity that is not changing is your anchor.
• Check that the mean lies in between. If your target value is not between the two ingredients, the question has been misread.
• Reuse the rule in other topics. Average rates in simple and compound interest and cost in profit and loss problems use the same cross.

Aim for 40 to 50 seconds. With practice, alligation becomes faster than forming equations.

The full mixture and alligation topic test is on PrepMatic (about 15 questions, 30 minutes). Return to the Quantitative Aptitude guide for the full topic map, or the bank exam hub for each exam's pattern.

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