Alligation or Mixture problems
- 1. A cask full of wine from which 8 litres are drawn and is then filled with water. This operation is performed three more times. The ratio of quantity of wine left in the cask to that of the water is 16: 81. How much wine did the cask hold originally?
Options- A. 42 litres
- B. 32 litres
- C. 24 litres
- D. 18 litres Discuss
Correct Answer: 24 litres
Explanation:
Let A liters wine cask hold originally, then
A[1 - (8 / A)]4 / A = 16 / 81
? (1 - (8 / A))4 = (2 / 3 )4
? (1 - (8 / A)) = (2 / 3)
? (8 / A) = (1 - (2 /3))
? (8 / A) = (1 / 3)
? A = 24 liters
- 2. Rs. 675 was divided among 75 boys and girls. Each boy gets Rs. 20 whereas a girl gets Rs. 5. Find the number of boys and girls.
Options- A. 20 , 55
- B. 15 , 60
- C. 25 , 50
- D. 30 , 45 Discuss
Correct Answer: 20 , 55
Explanation:
Average money per head (boy or girl) = Rs. (675 / 75) = Rs. 9
Number of boys = 4 / (4 + 11) × 75 = 20
Number of girls = 11 / (4 + 11) × 75 = 55.
- 3. A sum of Rs. 41 was divided among 50 boys and girls. Each boy gets 90 paise and a girl 65 paise. The number of boys is ?
Options- A. 16
- B. 34
- C. 14
- D. 36 Discuss
Correct Answer: 34
Explanation:
- 4. Some amount out of Rs. 7000 was lent at 6 % p.a. and the remaining at 4 % p. a. If the total simple interest from both the fractions in 5 years was Rs. 1600, the sum lent at 6 % p. a. was ?
Options- A. Rs. 2000
- B. Rs. 5000
- C. Rs. 3500
- D. None of these Discuss
Correct Answer: Rs. 2000
Explanation:
- 5. Sugar at Rs. 15 per kg is mixed with sugar at Rs. 20 per kg in the ratio 2 : 3. Find the price per kg of the mixture?
Options- A. Rs. 18
- B. Rs. 16
- C. Rs. 17
- D. Rs. 19 Discuss
Correct Answer: Rs. 18
Explanation:
- 6. Kantilal mixes 80 kg of sugar worth of Rs. 6·75 per kg with 120 kg worth of Rs. 8 per kg. At what rate shall he sell the mixture to gain 20 %?
Options- A. Rs. 7·50
- B. Rs. 9
- C. Rs. 8·20
- D. Rs. 8·85 Discuss
Correct Answer: Rs. 9
Explanation:
According to question ,
Total C. P. of 200 kg of mixture = Rs. (80 × 6·75 + 120 × 8)
Total C. P. of 200 kg of mixture = Rs. 1500
Average rate = Rs. 7·50 per kg
Required rate = 120% of Rs. 7·50
Required rate = Rs. 9 per kg.
- 7. A grocer buys two kind of rice at Rs. 1·80 and Rs. 1·20 per kg respectively. In what proportion should these be mixed, so that by selling the mixture at Rs. 1·75 per kg, 25 % may be gained?
Options- A. 2 : 1
- B. 3 : 2
- C. 3 : 4
- D. 1 : 2 Discuss
Correct Answer: 1 : 2
Explanation:
- 8. 15 liters of a mixture contains 20 % alcohol and the rest water. If 3 liters of water be mixed in it, the % of alcohol in the new mixture will be ?
Options- A. 17
- B. 16 2 3
- C. 18 1 2
- D. 15 Discuss
Correct Answer: 16 2 3
Explanation:
- 9. A dishonest milkman professes to sell his milk at C. P. But he mixes it with water and thereby gains 25 %. The % of water in the mixture is ?
Options- A. 25%
- B. 20%
- C. 4%
- D. None of these Discuss
Correct Answer: 20%
Explanation:
- 10. In what ratio must a grocer mix sugar at 72 paise per kg with sugar at 48 paise per kg. So that by selling the mixture at
63 paise per kg he may gain 1 of his out-lay? 6
Options- A. 1 : 3
- B. 3 : 1
- C. 2 : 3
- D. 3 : 2 Discuss
Correct Answer: 1 : 3
Explanation:
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