Mixture and Alligation Questions for RRB NTPC Exam: Download Free PDF

If you are preparing for the RRB NTPC or any other Railway exam, you already know that the Mathematics section is your best ticket to the final merit list. Inside this section, “Mixture and Alligation” is a chapter that many students skip because word problems about mixing milk, water, and expensive rice look very confusing.

They think it requires pages of rough work and long formulas. But here is a big secret: this entire chapter runs on a single 5-second trick! Once you learn the famous “Cross Method,” you can solve the hardest questions simply by subtracting two numbers. Even better, this trick also helps you quickly solve questions from other chapters like Profit & Loss, Simple Interest, and Averages.

In this blog, we have explained this topic in the simplest words possible and provided the top exam-level questions that the Railway Recruitment Board (RRB) repeats in almost every shift.

What is Mixture and Alligation? (Explained in Simple Words)

You do not need to be a math genius to understand this. Let us break it down using a daily life example.

• Mixture: This is simple. When you mix two different things together (like pure milk and water, or cheap rice and expensive rice), you get a mixture.
• Alligation: This is the magic trick used to find out the Ratio of the mixture.

The “Cross Method” Magic Trick: Suppose a shopkeeper mixes cheap rice (Rs. 30/kg) with expensive rice (Rs. 50/kg) and wants to sell the mixed rice at Rs. 40/kg. What ratio should he mix them in? Instead of making long ‘x’ and ‘y’ equations, you just write it like an ‘X’ (cross):

1. Put the Cheap Price on the left (30).
2. Put the Expensive Price on the right (50).
3. Put the Mixture Price in the exact center (40).
4. Now, simply cross-subtract! (50 – 40 = 10) and (40 – 30 = 10).
5. The ratio is 10:10, which means 1:1.

That’s it! You just found the answer in 5 seconds.

Important Mixture and Alligation Questions for RRB NTPC

Now that you know the basic trick, it is time to practice! Grab a pen and try to solve these top highly repeated exam-level questions. These perfectly match the RRB NTPC exam format and difficulty.

Q1. In what ratio must rice at Rs. 30 per kg be mixed with rice at Rs. 40 per kg so that the final mixture is worth Rs. 33 per kg?

(A) 7 : 3
(B) 3 : 7
(C) 4 : 3
(D) 3 : 4

Answer: (A) 7 : 3

Explanation: Use the cross method.

Cheap rice = Rs. 30
Expensive rice = Rs. 40
Mean price = Rs. 33

Cross subtract:
40 – 33 = 7
33 – 30 = 3

So, the required ratio = 7 : 3.

Q2. A grocer mixes two varieties of wheat costing Rs. 60 per kg and Rs. 80 per kg in the ratio 3 : 2. What is the price of the final mixture?

(A) Rs. 66
(B) Rs. 68
(C) Rs. 70
(D) Rs. 72

Answer: (B) Rs. 68

Explanation: Use the weighted average method.

(60 × 3) + (80 × 2)
= 180 + 160
= 340

Total ratio units = 3 + 2 = 5

Price of mixture = 340 / 5 = Rs. 68 per kg.

Q3. In what ratio must a milkman mix free water with pure milk to gain a 20% profit by selling the mixture at the cost price of pure milk?

(A) 1 : 4
(B) 1 : 5
(C) 5 : 1
(D) 4 : 1

Answer: (B) 1 : 5

Explanation: When a milkman sells the mixture at the cost price of milk, the ratio of Water : Milk becomes equal to the profit percentage.

Profit = 20%

So,
Water : Milk = 20 : 100 = 1 : 5.

Q4. A 40-liter mixture of milk and water contains 10% water. How much extra water must be added to make the water exactly 20% in the new mixture?

(A) 4 liters
(B) 5 liters
(C) 8 liters
(D) 10 liters

Answer: (B) 5 liters

Explanation: Milk quantity always remains fixed.

Old milk = 90% of 40
= 36 liters

In the new mixture, water is 20%.
So, milk becomes 80%.

80% of new mixture = 36

New mixture = (36 / 80) × 100
= 45 liters

Extra water added = 45 – 40
= 5 liters.

Q5. A trader has 50 kg of sugar. He sells a part of it at 8% profit and the rest at 18% profit. He gains 14% on the whole. What is the quantity sold at 18% profit?

(A) 20 kg
(B) 25 kg
(C) 30 kg
(D) 35 kg

Answer: (C) 30 kg

Explanation: Apply the cross method.

Left = 8%
Right = 18%
Mean = 14%

Cross subtract:
18 – 14 = 4
14 – 8 = 6

Ratio = 4 : 6 = 2 : 3

Total units = 5

Total sugar = 50 kg
1 unit = 10 kg

Quantity sold at 18% profit = 3 units
= 3 × 10
= 30 kg.

Q6. Two vessels A and B contain acid and water in the ratio 4 : 1 and 2 : 3. In what ratio should these two be mixed to get a new mixture containing half acid and half water?

(A) 1 : 2
(B) 1 : 3
(C) 2 : 1
(D) 3 : 1

Answer: (B) 1 : 3

Explanation: Acid in vessel A = 4/5
Acid in vessel B = 2/5
Target acid = 1/2

Apply cross method:

(1/2 – 2/5) = 1/10
(4/5 – 1/2) = 3/10

Ratio = 1/10 : 3/10
= 1 : 3.

Q7. How many kg of salt at Rs. 42 per kg must be mixed with 25 kg of salt at Rs. 24 per kg so that selling the mixture at Rs. 40 per kg gives a profit of 25%?

(A) 15 kg
(B) 20 kg
(C) 25 kg
(D) 30 kg

Answer: (B) 20 kg

Explanation: First find the Cost Price of the mixture.

CP = SP / 1.25
= 40 / 1.25
= Rs. 32

Now apply cross method:

42 – 32 = 10
32 – 24 = 8

Ratio = 8 : 10 = 4 : 5

25 kg corresponds to 5 parts.

1 part = 25 / 5 = 5 kg

Required salt = 4 parts
= 4 × 5
= 20 kg.

Q8. The average marks of students in a class is 68. The average marks of girls is 80 and that of boys is 60. What is the percentage of boys in the class?

(A) 40%
(B) 50%
(C) 60%
(D) 70%

Answer: (C) 60%

Explanation: Use alligation on averages.

Girls = 80
Boys = 60
Average = 68

Cross subtract:
68 – 60 = 8
80 – 68 = 12

Girls : Boys = 8 : 12
= 2 : 3

Total parts = 5

Percentage of boys = (3 / 5) × 100
= 60%.

Q9. A vessel contains 60 liters of pure milk. 6 liters of milk is taken out and replaced with water. This process is repeated one more time. How much milk is left in the vessel?

(A) 48.6 liters
(B) 49.2 liters
(C) 50 liters
(D) 54 liters

Answer: (A) 48.6 liters

Explanation: Use the replacement formula:

Remaining milk
= Initial × (1 – Taken/Total)^n

= 60 × (1 – 6/60)^2
= 60 × (9/10)^2
= 60 × 81/100
= 48.6 liters.

Q10. In a zoo, there are some rabbits and some pigeons. If their heads are counted, there are 100. If their legs are counted, there are 290. How many rabbits are there?

(A) 40
(B) 45
(C) 50
(D) 55

Answer: (B) 45

Explanation: Pigeons have 2 legs.
Rabbits have 4 legs.

Average legs per animal
= 290 / 100
= 2.9

Apply alligation:

4 – 2.9 = 1.1
2.9 – 2 = 0.9

Pigeons : Rabbits = 1.1 : 0.9
= 11 : 9

Total parts = 20

Total animals = 100
1 part = 5

Number of rabbits = 9 × 5
= 45.

5 Simple Tips to Prepare Mixture and Alligation

You do not need to memorize heavy formulas. Just play smart with these 5 easy tips:

• Never Mix CP and SP: This is where 90% of students fail! If you put Cost Price on the left and right sides of the cross, the center value MUST also be the Cost Price. If the question gives the Selling Price, convert it to CP first.
• The “Constant Item” Rule: In questions where you add extra water to a milk mixture, always solve using the Milk quantity because the amount of milk never changed!
• Find Hidden Alligations: The cross method is not just for milk and water. You can use it to find ratios in Simple Interest, Averages, Profit/Loss, and even speed/distance problems!
• Memorize the Water Profit Trick: If you sell mixed milk at the cost price of pure milk, your profit % is exactly equal to the ratio of water added. You do not even need a pen for this!
• Practice Previous Year Papers: The RRB Board rarely creates new math logic. They just change the numbers. Practice old NTPC, Group D, and ALP papers to master the repeating patterns.

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FAQs: Mixture and Alligation for RRB NTPC

1. Is Mixture and Alligation a difficult chapter for RRB NTPC?

No, not at all! Once you learn how to draw the cross (Alligation Rule), it becomes one of the fastest and easiest chapters to solve without writing long steps.

2. How many questions can I expect from this topic in CBT 1 and CBT 2?

You can comfortably expect 1 to 2 direct questions from this chapter. Additionally, you will use its shortcuts to solve percentage and average questions quickly.

3. What is the difference between Mixture and Alligation?

“Mixture” is the actual physical act of mixing two things (like sugar and salt). “Alligation” is just a mathematical shortcut trick (the cross method) used to find their mixing ratio.

4. Can I use the Alligation trick if three things are mixed?

Yes, but it is slightly advanced. For RRB NTPC, the examiner almost always asks about mixing just two items. Stick to the basic two-item cross method.

5. Are these questions useful for SSC and other Railway exams too?

Yes, 100%! The syllabus and logic for Mixture and Alligation are exactly the same across RRB NTPC, Group D, ALP, and SSC exams like CGL and CHSL.