Q1): In what ratio should 20% and 50% alcohol solutions be mixed to get a 30% alcohol solution?
A) 1 : 2
B) 2 : 1
C) 3 : 2
D) 4 : 1
Answer: B) 2 : 1
Explanation:
- Step 1: Use alligation ratio = (Higher − Mean) : (Mean − Lower)
- Step 2: Lower = 20, Mean = 30, Higher = 50
- Step 3: Ratio = (50 − 30) : (30 − 20) = 20 : 10
- Step 4: Simplify = 2 : 1
- Final: So 20% : 50% = 2 : 1
Q2): Rice at ₹40/kg is mixed with rice at ₹60/kg to get a mixture worth ₹48/kg. Find the ratio of ₹40 rice to ₹60 rice.
A) 2 : 3
B) 3 : 2
C) 4 : 1
D) 5 : 3
Answer: B) 3 : 2
Explanation:
- Step 1: Apply alligation for prices
- Step 2: Cheaper = 40, Mean = 48, Dearer = 60
- Step 3: Ratio = (60 − 48) : (48 − 40) = 12 : 8
- Step 4: Simplify = 3 : 2
- Final: ₹40 rice : ₹60 rice = 3 : 2
Q3): A 10 L solution contains 40% alcohol. How much water should be added to make it 25% alcohol?
A) 4 L
B) 5 L
C) 6 L
D) 8 L
Answer: C) 6 L
Explanation:
- Step 1: Alcohol in 10 L = 40% of 10 = 4 L
- Step 2: After adding x L water, total = 10 + x
- Step 3: New % = 25% ⇒ alcohol = 25% of (10 + x)
- Step 4: 0.25(10 + x) = 4 ⇒ 2.5 + 0.25x = 4 ⇒ x = 6
- Final: Add 6 L water
Q4): Sugar at ₹30/kg is mixed with sugar at ₹15/kg to get a mixture worth ₹24/kg. Find the ratio of ₹15 sugar to ₹30 sugar.
A) 3 : 2
B) 2 : 3
C) 1 : 2
D) 4 : 1
Answer: B) 2 : 3
Explanation:
- Step 1: Use alligation ratio = (Dearer − Mean) : (Mean − Cheaper)
- Step 2: Cheaper = 15, Mean = 24, Dearer = 30
- Step 3: Ratio = (30 − 24) : (24 − 15) = 6 : 9
- Step 4: Simplify = 2 : 3
- Final: ₹15 : ₹30 = 2 : 3
Q5): 3 L of 10% salt solution is mixed with 2 L of 25% salt solution. What is the final salt percentage?
A) 14%
B) 15%
C) 16%
D) 18%
Answer: C) 16%
Explanation:
- Step 1: Salt in first = 10% of 3 = 0.3 L
- Step 2: Salt in second = 25% of 2 = 0.5 L
- Step 3: Total salt = 0.3 + 0.5 = 0.8 L
- Step 4: Total solution = 3 + 2 = 5 L ⇒ % = (0.8/5)×100 = 16%
- Final: Final concentration = 16%
Q6): Tea at ₹200/kg is mixed with tea at ₹150/kg to get a mixture worth ₹180/kg. Find ratio of ₹150 tea to ₹200 tea.
A) 3 : 2
B) 2 : 3
C) 1 : 2
D) 4 : 3
Answer: B) 2 : 3
Explanation:
- Step 1: Apply alligation on prices
- Step 2: Cheaper = 150, Mean = 180, Dearer = 200
- Step 3: Ratio = (200 − 180) : (180 − 150) = 20 : 30
- Step 4: Simplify = 2 : 3
- Final: ₹150 : ₹200 = 2 : 3
Q7): Pure milk is mixed with water to get a mixture containing 70% milk. Find the ratio of milk to water.
A) 5 : 2
B) 7 : 3
C) 3 : 7
D) 2 : 5
Answer: B) 7 : 3
Explanation:
- Step 1: Treat milk as 100% and water as 0% milk
- Step 2: Mean milk% = 70
- Step 3: Ratio (100% : 0%) = (70 − 0) : (100 − 70) = 70 : 30
- Step 4: Simplify = 7 : 3
- Final: Milk : Water = 7 : 3
Q8): An alloy has 80% copper and another has 50% copper. In what ratio should they be mixed to get 65% copper alloy?
A) 1 : 2
B) 2 : 1
C) 1 : 1
D) 3 : 2
Answer: C) 1 : 1
Explanation:
- Step 1: Use alligation on copper %
- Step 2: Lower = 50, Mean = 65, Higher = 80
- Step 3: Ratio = (80 − 65) : (65 − 50) = 15 : 15
- Step 4: Simplify = 1 : 1
- Final: Mix in equal quantities
Q9): 8 L milk at ₹40/L is mixed with 12 L milk at ₹30/L. Find the average price per litre of the mixture.
A) ₹32
B) ₹33
C) ₹34
D) ₹35
Answer: C) ₹34
Explanation:
- Step 1: Total cost = 8×40 + 12×30
- Step 2: Total cost = 320 + 360 = 680
- Step 3: Total quantity = 8 + 12 = 20 L
- Step 4: Average price = 680 ÷ 20 = 34
- Final: Mixture price = ₹34/L
Q10): A 30 L mixture of milk and water is in the ratio 2:1. How much water is in the mixture?
A) 8 L
B) 10 L
C) 12 L
D) 15 L
Answer: B) 10 L
Explanation:
- Step 1: Ratio milk:water = 2:1 ⇒ total parts = 3
- Step 2: Water part = 1 out of 3
- Step 3: Water = (1/3)×30 = 10 L
- Step 4: Check: milk would be 20 L, total 30 L
- Final: Water = 10 L
Q11): 4 kg of 12% salt solution is mixed with 6 kg of 18% salt solution. Find the final salt percentage.
A) 14.4%
B) 15.6%
C) 16.8%
D) 17.2%
Answer: B) 15.6%
Explanation:
- Step 1: Salt in first = 12% of 4 = 0.48 kg
- Step 2: Salt in second = 18% of 6 = 1.08 kg
- Step 3: Total salt = 0.48 + 1.08 = 1.56 kg; total mixture = 10 kg
- Step 4: % salt = (1.56/10)×100 = 15.6%
- Final: Final concentration = 15.6%
Q12): In what ratio should 10% and 20% solutions be mixed to get a 14% solution?
A) 2 : 3
B) 3 : 2
C) 4 : 1
D) 1 : 4
Answer: B) 3 : 2
Explanation:
- Step 1: Alligation ratio = (Higher − Mean) : (Mean − Lower)
- Step 2: Lower = 10, Mean = 14, Higher = 20
- Step 3: Ratio = (20 − 14) : (14 − 10) = 6 : 4
- Step 4: Simplify = 3 : 2
- Final: 10% : 20% = 3 : 2
Q13): Pulses at ₹70/kg and ₹50/kg are mixed to get a mixture worth ₹60/kg. Find the ratio of ₹70 pulses to ₹50 pulses.
A) 1 : 2
B) 2 : 1
C) 1 : 1
D) 3 : 2
Answer: C) 1 : 1
Explanation:
- Step 1: Use alligation on prices
- Step 2: Cheaper = 50, Mean = 60, Dearer = 70
- Step 3: Ratio (₹70 : ₹50) = (60 − 50) : (70 − 60) = 10 : 10
- Step 4: Simplify = 1 : 1
- Final: Mix equal quantities
Q14): A container has 15 L acid solution of 60% concentration. If 5 L water is added, what is the new concentration?
A) 40%
B) 45%
C) 48%
D) 50%
Answer: B) 45%
Explanation:
- Step 1: Pure acid in 15 L = 60% of 15 = 9 L
- Step 2: Water added = 5 L ⇒ new total = 15 + 5 = 20 L
- Step 3: Pure acid remains 9 L (only water added)
- Step 4: New % = (9/20)×100 = 45%
- Final: New concentration = 45%
Q15): A mixture costs ₹55/kg and is made by mixing ₹50/kg and ₹65/kg qualities. Find the ratio of ₹50 to ₹65 in the mixture.
A) 1 : 2
B) 2 : 1
C) 3 : 1
D) 1 : 3
Answer: B) 2 : 1
Explanation:
- Step 1: Apply alligation on prices
- Step 2: Cheaper = 50, Mean = 55, Dearer = 65
- Step 3: Ratio = (65 − 55) : (55 − 50) = 10 : 5
- Step 4: Simplify = 2 : 1
- Final: ₹50 : ₹65 = 2 : 1
Q16): 9 L of 30% alcohol solution is mixed with some 45% solution to make 15 L of 36% solution. How many litres of 45% solution are used?
A) 4 L
B) 5 L
C) 6 L
D) 7 L
Answer: C) 6 L
Explanation:
- Step 1: Total mixture = 15 L; already have 9 L
- Step 2: So 45% solution used = 15 − 9 = 6 L
- Step 3: Check alcohol: 9×0.30 = 2.7 L and 6×0.45 = 2.7 L
- Step 4: Total alcohol = 5.4 L; 5.4/15 = 0.36 = 36%
- Final: 45% solution used = 6 L
Q17): 7 kg of mixture at ₹25/kg is mixed with 3 kg at ₹20/kg. Find the average price per kg.
A) ₹22.5
B) ₹23
C) ₹23.5
D) ₹24
Answer: C) ₹23.5
Explanation:
- Step 1: Total cost = 7×25 + 3×20
- Step 2: Total cost = 175 + 60 = 235
- Step 3: Total quantity = 7 + 3 = 10 kg
- Step 4: Average price = 235 ÷ 10 = 23.5
- Final: Average price = ₹23.5/kg
Q18): A 20 L mixture contains 25% alcohol. If 4 L of mixture is removed and replaced with water (one time), what is the new alcohol percentage?
A) 18%
B) 19%
C) 20%
D) 21%
Answer: C) 20%
Explanation:
- Step 1: Initial alcohol = 25% of 20 = 5 L
- Step 2: Removed 4 L mixture ⇒ alcohol removed = 25% of 4 = 1 L
- Step 3: Remaining alcohol = 5 − 1 = 4 L (now total is 16 L)
- Step 4: Replace 4 L with water ⇒ total back to 20 L, alcohol still 4 L
- Final: New % = (4/20)×100 = 20%
Q19): Wheat at ₹18/kg is mixed with wheat at ₹22/kg to get a mixture worth ₹20/kg. If total mixture is 40 kg, how much ₹22 wheat is used?
A) 16 kg
B) 18 kg
C) 20 kg
D) 24 kg
Answer: C) 20 kg
Explanation:
- Step 1: Apply alligation on prices
- Step 2: Cheaper = 18, Mean = 20, Dearer = 22
- Step 3: Ratio (₹18 : ₹22) = (22 − 20) : (20 − 18) = 2 : 2 = 1 : 1
- Step 4: Total 40 kg split equally ⇒ ₹22 wheat = 40/2 = 20 kg
- Final: ₹22 wheat used = 20 kg
Q20): 1 L pure juice is mixed with 3 L water. What is the percentage of juice in the mixture?
A) 20%
B) 25%
C) 30%
D) 33.33%
Answer: B) 25%
Explanation:
- Step 1: Juice = 1 L, water = 3 L
- Step 2: Total mixture = 1 + 3 = 4 L
- Step 3: Juice fraction = 1/4
- Step 4: Juice % = (1/4)×100 = 25%
- Final: Juice percentage = 25%