SSC CGL Preparation – Day 13

MCQs: Mixtures and Alligations

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Q1. In what ratio must tea costing ₹60/kg be mixed with tea costing ₹90/kg so that the mixture costs ₹84/kg?

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

Solution: $$\frac{90 – 84}{84 – 60} = \frac{6}{24} = 1:4 \Rightarrow \text{Answer: Option C}8$$

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Q2. A 40 L mixture contains milk and water in the ratio 3:1. 8 L is taken out and replaced with water. What is the new ratio of milk to water?

A) 2:1
B) 8:5
C) 9:7
D) 7:5

Solution:
Milk in 8 L = 6 L; Water = 2 L
Remaining Milk = 30 – 6 = 24 L
Remaining Water = 10 – 2 + 8 = 16 L ⇒$$\text{Ratio} = 24:16 = 3:2 \Rightarrow \text{Answer: Not listed (Correct ratio is 3:2)}$$

Let’s correct options.

✅ Corrected Options:
A) 3:2
B) 5:3
C) 8:5
D) 9:7

Answer: Option A

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Q3. The cost of type 1 rice is ₹20/kg and type 2 rice is ₹30/kg. If the two types are mixed in the ratio 2:3, what is the price per kg of the mixture?

A) ₹24
B) ₹26
C) ₹25
D) ₹22

Solution: $$= \frac{(2 \times 20 + 3 \times 30)}{2 + 3} = \frac{40 + 90}{5} = ₹26 \Rightarrow \text{Answer: Option B}$$

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Q4. A dishonest dealer adds water to milk to earn a profit of 25%. What is the ratio of water to milk?

A) 1:5
B) 1:4
C) 1:3
D) 1:2

Solution: $$\text{Water:Milk} = \frac{Profit}{100 + Profit} = \frac{25}{125} = 1:5 \Rightarrow \text{Answer: Option A}$$

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Q5. A container contains 60 L of milk. 12 L is taken out and replaced with water. This operation is repeated 2 more times. Find the final quantity of milk.

A) 32.4 L
B) 35.2 L
C) 30.7 L
D) 34.1 L

Solution: $$= 60 \times \left(1 – \frac{12}{60} \right)^3 = 60 \times \left(\frac{4}{5}\right)^3 = 60 \times \frac{64}{125} = 30.72 L \Rightarrow \text{Answer: Option C}$$

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Q6. Two types of sugar costing ₹20/kg and ₹32/kg are mixed to get a mixture worth ₹28/kg. What is the ratio of cheaper to costlier?

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

Solution: $$\frac{32 – 28}{28 – 20} = \frac{4}{8} = 1:2 \Rightarrow \text{Answer: Option A}$$

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Q7. In a 72 L mixture of milk and water, milk is 75%. How much water must be added to make the ratio 2:1?

A) 6 L
B) 9 L
C) 12 L
D) 18 L

Solution:
Milk = 75% of 72 = 54 L, Water = 18 L
Let x L water added $$\frac{54}{18 + x} = \frac{2}{1} \Rightarrow 54 = 36 + 2x \Rightarrow 18 = 2x \Rightarrow x = 9 L \Rightarrow \text{Answer: Option B}$$

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Q8. If a 30 L solution has alcohol and water in the ratio 3:2, how much alcohol is there?

A) 15 L
B) 18 L
C) 12 L
D) 9 L

Solution: $$\text{Total parts} = 3 + 2 = 5 \Rightarrow \text{Alcohol} = \frac{3}{5} \times 30 = 18 L \Rightarrow \text{Answer: Option B}$$

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Q9. A 20 L mixture contains milk and water in the ratio 5:3. 4 L of mixture is removed and replaced with water. What is the new ratio?

A) 2:1
B) 4:3
C) 3:2
D) 25:19

Solution:
Milk in 4L = (5/8)×4 = 2.5 L, Water = 1.5 L
After removal: Milk = 10 – 2.5 = 7.5, Water = 6 – 1.5 + 4 = 8.5 $$\Rightarrow \text{Ratio} = 7.5:8.5 = 15:17 \Rightarrow \text{Not in options — Let’s correct} \Rightarrow \text{Answer: 15:17}$$

✅ Corrected Option:
D) 15:17

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Q10. A milkman sells milk at cost price but adds water and gains 20%. What is the ratio of water to milk?

A) 1:5
B) 1:4
C) 1:6
D) 1:3

Solution: $$\text{Water:Milk} = \frac{20}{120} = 1:6 \Rightarrow \text{Answer: Option C}$$