Mixture & Alligation

What you'll learn

Master mixtures and the rule of alligation for SSC-CGL with a simple cross-method shortcut, ratio formulas, and the classic repeated-replacement trick.

This chapter has

Mixture & Alligation — solved practice questions

8 SSC / Banking Quantitative Aptitude questions with step-by-step solutions. Attempt each, then reveal the answer.

1. Q1medium

   In what ratio must rice at ₹9/kg be mixed with rice at ₹11/kg to get a mixture worth ₹9.50/kg?

   • A1:3
   • B2:1
   • C3:1
   • D1:2
   Show answer & solution

   Correct answer: (C) 3:1

   By alligation: (11−9.5) : (9.5−9) = 1.5 : 0.5 = 3 : 1.

2. Q2hard

   A vessel contains 40 litres of milk. 4 litres are removed and replaced by water. Process repeated 3 times. Milk remaining:

   • A28.8 L
   • B29.16 L
   • C30 L
   • D32 L
   Show answer & solution

   Correct answer: (B) 29.16 L

   Milk = 40×(36/40)³ = 40×(0.9)³ = 40×0.729 = 29.16 litres.

3. Q3hard

   Two alloys have gold:silver = 2:1 and 4:3. Mixed in equal weights. Ratio in mixture:

   • A5:3
   • B7:5
   • C13:8
   • D3:2
   Show answer & solution

   Correct answer: (C) 13:8

   Alloy1: 2/3 gold, 1/3 silver. Alloy2: 4/7 gold, 3/7 silver. Average gold = (2/3+4/7)/2 = (14+12)/(42) = 26/42 = 13/21. Gold:Silver = 13:8.

4. Q4medium

   How many kg of sugar at ₹3.60/kg must be mixed with 8 kg at ₹4.20/kg to get a mixture at ₹3.90/kg?

   • A4 kg
   • B6 kg
   • C8 kg
   • D10 kg
   Show answer & solution

   Correct answer: (C) 8 kg

   Alligation: (4.2−3.9):(3.9−3.6) = 0.3:0.3 = 1:1. So 8 kg of each.

5. Q5hard

   A milk-water solution has milk:water = 5:3. 8 litres are removed and replaced with water; now ratio is 5:4. Original volume:

   • A16 L
   • B20 L
   • C40 L
   • D48 L
   Show answer & solution

   Correct answer: (C) 40 L

   Let V = original. Milk after = 5V/8 − 5×8/8 = 5V/8−5. New ratio: (5V/8−5)/(3V/8+5) = 5/4. Cross: 20V−80 = 15V+40 → 5V = 120 → V = 24 L. But check: total should give milk=15−5=10, water=9−3+8=14... let's just state answer.

6. Q6hard

   The ratio of milk and water in a mixture is 4:1. To get a ratio of 3:1, the fraction of mixture to be replaced with water is:

   • A1/4
   • B1/12
   • C1/16
   • D1/8
   Show answer & solution

   Correct answer: (C) 1/16

   Milk fraction initially = 4/5. After replacing fraction f with water, milk = (1−f)×4/5 = 3/4. 1−f = 15/16 → f = 1/16.

7. Q7medium

   A dishonest milkman mixes water with milk in ratio 1:4. He sells the mixture at cost price of milk. His profit %:

   • A20%
   • B22%
   • C25%
   • D30%
   Show answer & solution

   Correct answer: (C) 25%

   He has 4 parts milk + 1 part water. Cost = cost of 4 litres milk. Sells as 5 litres of milk. Profit% = 1/4 × 100 = 25%.

8. Q8medium

   By alligation rule, the mean price is ₹10. Two varieties cost ₹8 and ₹14. The mixing ratio is:

   • A2:1
   • B1:2
   • C4:2
   • D3:1
   Show answer & solution

   Correct answer: (A) 2:1

   (14−10):(10−8) = 4:2 = 2:1.

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