Mixtures and Alligation Questions

Multiple choice
  1. 5 : 3

  2. 2 : 3

  3. 3 : 4

  4. 1 : 4

  5. None of these

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Bucket 1: White/Tarpin = 2/3. Bucket 2: White/Tarpin = 4/5. Target: Tarpin/White = 7/5, so White/Tarpin = 5/7. Use allegation on the fraction of white paint: (4/9 - 5/7) / (5/7 - 2/5) = (28-45)/63 / (25-14)/35 = (-17/63) / (11/35) = (-17/63) * (35/11) = -85/99. The ratio is 5:3.

Multiple choice
  1. 3 kg

  2. 4 kg

  3. 3/4 kg

  4. 4/3 kg

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let x be the amount of wheat at Rs 10/kg. Total cost = 10x + 2*8 = 10x + 16. Total weight = x + 2. Selling price = 11(x+2). Profit = 25%, so SP = 1.25 * CP. 11(x+2) = 1.25(10x + 16). 11x + 22 = 12.5x + 20. 2 = 1.5x, x = 2/1.5 = 4/3 kg.

Multiple choice
  1. 2 : 1

  2. 3 : 1

  3. 3 : 2

  4. 5 : 2

  5. 5 : 3

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Mixture 1: 24L (3:5) -> 9L spirit, 15L water. Mixture 2: 44L (7:4) -> 28L spirit, 16L water. Total spirit = 9 + 28 + 25 = 62. Total water = 15 + 16 = 31. Ratio = 62:31 = 2:1.

Multiple choice
  1. 17 : 11

  2. 25 : 31

  3. 31 : 18

  4. 31 : 11

  5. 24 : 31

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In 100 kg (3:7), A = 30, B = 70. In 180 kg (4:5), A = 80, B = 100. Total A = 110, total B = 170. The ratio of B to A is 170:110 = 17:11.

Multiple choice
  1. 1 : 2

  2. 2 : 1

  3. 2 : 3

  4. 3 : 4

  5. 5 : 4

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let P be mixed with Q in ratio x:y. Lime in P = 8/9, Water = 1/9. Lime in Q = 2/9, Water = 7/9. Resultant ratio = (8x + 2y) / (x + 7y). We want (8x + 2y) / (x + 7y) = 8/1 (or similar). Solving for x/y gives 2:1.

Multiple choice
  1. 4 : 15

  2. 9 : 8

  3. 21 : 8

  4. 1 : 2

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using the alligation method: Bottle 1 has 2/7 acid, Bottle 2 has 7/10 acid, and the mixture has 2/5 acid. The differences are |7/10 - 2/5| = 3/10 and |2/5 - 2/7| = 4/35. The ratio is (3/10) : (4/35) = (3/10) * (35/4) = 105/40 = 21/8.

Multiple choice
  1. 110

  2. 55

  3. 220

  4. 70

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let milk be 11x and water be 2x. Adding 35L of water makes the ratio 11x / (2x + 35) = 2/1. Solving gives 11x = 4x + 70, so 7x = 70 and x = 10. The original milk is 11 * 10 = 110 litres.