Alligation or Mixture problems
- 1. A piece of an alloy of two metals (A and B) weighs 15 gms and costs Rs. 150. If the weights of the two metals be interchanged, the new alloy would be worth Rs. 120. If the price of metal A is Rs. 6 per gm, find the weight of the other metal in the original piece of alloy.
Options- A. 5 gms
- B. 8 gms
- C. 10 gms
- D. 12 gms Discuss
Correct Answer: 10 gms
Explanation:
If the two alloys are mixed, the mixture would contain 15 gms of each metal and it would cost Rs. (150 + 120) = Rs. 270.
Cost of (15 gms of metal A + 15 gms of metal B) = Rs. 270
Cost of (1 gm of metal A + 1 gm of metal B) = Rs. (270 / 15) = Rs. 18
Cost of 1 gm of metal B = Rs. (18 ? 6) = Rs. 12
Average cost of original piece of alloy = (150 / 15) = Rs. 10 per gm.
Quantity of metal / A Quantity of metal B = (2 / 4) = (1 / 2)
Quantity of metal B = 2 (1 + 2) × 15 = 10 gms.
- 2. A container of 90 liters with two liquids A and B, 60% of liquid A and 30% of liquid B are taken out of the vessel. This leaves the container 40% empty. Find the initial quantity of both liquids.
Options- A. 50 litres
- B. 54 litres
- C. 57 litres
- D. 60 litres Discuss
Correct Answer: 60 litres
Explanation:
Here withdrawal of liquid A and B result into making the container empty. Hence percentage of two liquids withdrawn are two components of the percentage by which the container becomes empty.
Applying the rule of alligation, we get
A : B = 10 : 20 or 1 : 2
Quantity of liquid = 1 (1 + 2) × 90 = 30
liters Quantity of liquid B = 90 ? 30 = 60 liters.
- 3. Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If mixture is worth Rs. 153 per kg, the price of the third variety per kg will be:
Options- A. 180
- B. 175.50
- C. 170
- D. 169.50 Discuss
Correct Answer: 175.50
Explanation:
Here first two varieties of tea are mixed in equal ratio.
So their average price = (126 + 135) /2 = Rs. 130.50
Let price of the third variety per kg be Rs. A; then now mixture is formed by two varieties one at Rs. 130.50 per kg and other at Rs. A per kg in the same ratio 2 : 2 i.e, 1 : 1
By the rule of alligation,
(A - 153) / (22.50) = 1
? A ? 153 = 22.50
? A = Rs. 175.50
- 4. A mixture of 20 kg of spirit and water contains 10 % water. How much water must be added to this mixture to raise the percentage of water to 25 %?
Options- A. 4 kg
- B. 5 kg
- C. 8 kg
- D. 30 kg Discuss
Correct Answer: 4 kg
Explanation:
- 5. A jar full of whisky contains 40 % of alcohol. A part of this whisky is replaced by another containing 19 % alcohol and now the percentage of alcohol was found to be 26. The quantity of whisky replaced is ?
Options- A. 2 5
- B. 1 3
- C. 2 3
- D. 3 5 Discuss
Correct Answer: 2 3
Explanation:
- 6. Rs. 1000 is lent out in two parts, one at 6 % simple interest and the other at 8 % simple interest. The yearly income is Rs. 75. The sum lent at 8 % is ?
Options- A. Rs. 250
- B. Rs. 500
- C. Rs. 750
- D. Rs. 600 Discuss
Correct Answer: Rs. 750
Explanation:
- 7. A man has whisky worth Rs. 22 a liter and another lot worth Rs. 18 a liter. Equal quantities of these are mixed with water to obtain a mixture of 50 liters worth Rs. 16 a liter. Find how much water the mixture contains?
Options- A. 5 litre
- B. 10 litre
- C. 15 litre
- D. 20 litre Discuss
Correct Answer: 10 litre
Explanation:
- 8. A man buys milk at Rs. 5 a litre and mixes it with water. By selling the mixture at Rs. 4 a litre he gains 121/2 % on his outlay. How much water did each litre of the mixture contain?
Options- A. 32 litre 45
- B. 13 litre 45
- C. 32 litre 13
- D. None of these Discuss
Correct Answer: 13 litre 45
Explanation:
- 9. 3 glasses of capacity 2 liters, 5 liters and 9 liters contain mixture of milk and water with milk concentrations 90 %, 80 % and 70 % respectively. The contents of 3 glasses are emptied into a large vessel. Find the milk concentration and ratio of milk to water in the resultant mixture ?
Options- A. 121 : 39
- B. 131 : 49
- C. 39 : 121
- D. 49 : 131 Discuss
Correct Answer: 121 : 39
Explanation:
- 10. From a cask of wine, containing 64 liters, 8 liters are drawn out and the cask is filled up with water. If the same process is repeated a second, then a third time, what will be the number of liters of wine left in the cask?
Options- A. 42 1 kg 8
- B. 42 3 kg 8
- C. 48 7 kg 8
- D. 42 7 kg 8 Discuss
Correct Answer: 42 7 kg 8
Explanation:
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