Mixtures and Alligation Questions

Multiple choice
  1. Option 1

  2. Option 2

  3. Option 3

  4. Option 4

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

Ethanol fractions are 5/7 in A, 7/13 in B, target 8/13. Alligation gives the ratio (8/13 - 7/13) : (5/7 - 8/13) = (1/13) : (9/91) = 7 : 9. This matches option D.

Multiple choice
  1. 12.5%

  2. 25%

  3. 37.5%

  4. 50%

  5. 62.5%

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

Interpreting the initial ratio as milk to water = 3:2, the 25 litres contain 15 litres milk and 10 litres water. Equalizing the quantities requires x = 5 litres of water, and restoring the original ratio requires y = 7.5 litres of milk, which is 50% more than x.

Multiple choice
  1. 96 L

  2. 88 L

  3. 108 L

  4. 72 L

  5. 84 L

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

Mixture A: 3 parts, M:W = 4:5 (4/9 milk). Mixture B: 4 parts, M:W = 5:7 (5/12 milk). Total milk = 3*(4/9) + 4*(5/12) = 4/3 + 5/3 = 3 parts. Total water = 3*(5/9) + 4*(7/12) = 5/3 + 7/3 = 4 parts. If 3 parts = 72 L, 1 part = 24 L. Water = 4 parts = 96 L.

Multiple choice
  1. (a) 17 10/11%

  2. (b) 18 10/11 %

  3. (c) 16 10 / 11%

  4. (d) 1910 / 11%

  5. (e) 2010 / 11%

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

The first mixture contains 2 x 15% = 0.3 gallons of water, and the second contains 3 x 8% = 0.24 gallons. Adding 0.5 gallons of water gives 1.04 gallons of water in 5.5 gallons of mixture. The percentage is 1.04/5.5 x 100 = 18 10/11%.

Multiple choice
  1. (a) 108L

  2. (b) 72L

  3. (c) 80L

  4. (d) 96L

  5. (e) 84L

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

The formula for replacement is: Final quantity of beer / Initial quantity = (1 - x/V)^n. Here, 125/216 = (1 - 16/V)^3. Taking the cube root, 5/6 = 1 - 16/V. Thus, 16/V = 1/6, so V = 96L.

Multiple choice
  1. (a) 77L

  2. (b) 44L

  3. (c) 55L

  4. (d) 66L

  5. (e) 33L

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

Let initial quantity be 11x. Milk = 7x, Water = 4x. Remove 11L: Milk removed = 7/11 * 11 = 7, Water removed = 4. Remaining: Milk = 7x - 7, Water = 4x - 4. Add 4L milk: Milk = 7x - 3, Water = 4x - 4. Ratio (7x-3)/(4x-4) = 2/1. 7x - 3 = 8x - 8. x = 5. Initial quantity = 11 * 5 = 55L.

Multiple choice
  1. (a) 2 : 5

  2. (b) 3 : 5

  3. (c) 1 : 3

  4. (d) 2 : 3

  5. (e) 4 : 5

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

Using alligation on alcohol: Vessel A has 5/8 alcohol, Vessel B has 1/4 (2/8) alcohol. Target is 11/32. (11/32 - 8/32) : (20/32 - 11/32) = 3/32 : 9/32 = 3:9 = 1:3.

Multiple choice
  1. 1.50 kg

  2. 1.30 kg

  3. 1.40 kg

  4. 1.25 kg

  5. 1.75 kg

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

Formula for remaining amount: A = P(1 - r/100)^n. Here, A = 512, r = 20, n = 4. 512 = P(1 - 0.2)^4 = P(0.8)^4 = P(0.4096). P = 512 / 0.4096 = 1250 grams = 1.25 kg.