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- Question
- 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
- Correct Answer
- 175.50
ExplanationHere 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 - 1. 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
- 2. 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
- 3. A vessel contains mixture of liquids A and B in the ratio 3: 2. When 20 litres of the mixture is taken out and replaced by 20 litres of liquid B, the ratio changes to 1: 4. How many litres of liquid A was there initially present in the vessel?
Options- A. 12 litres
- B. 18 litres
- C. 24 litres
- D. 22 litres Discuss
- 4. From a cask of wine containing 25 litres, 5 litres are withdrawn and the cask is refilled with water. The process is repeated a second and then a third time. Find the quantity of wine left in the cask and also the ratio of wine to water in the resulting mixture.
Options- A. 61 : 64
- B. 16 : 46
- C. 46 : 16
- D. 64 : 61 Discuss
- 5. A person covers a distance of 100 kms in 10 hours, partly by walking at 7 km/hr and rest by running at 12 km/hr. Find the distance covered in each part.
Options- A. 48 kms
- B. 72 kms
- C. 108 kms
- D. 124 kms Discuss
- 6. 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
- 7. 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
- 8. 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
- 9. 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
- 10. 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
Alligation or Mixture problems
Search Results
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.
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.
Correct Answer: 18 litres
Explanation:
21.% of liquid B initially present in the vessel = 2 / (3 + 2) × 100 = 40%
% of liquid B finally present in the vessel = 4 / (1 + 4) × 100 = 80%
The second solution is liquid B which is being mixed and it has 100% liquid B.
80% of liquid B present in the resultant mixture may be taken as average percentage. So, using rule of alligation on liquid B per cent, we can write,
or 1 : 2
The ratio of liquid left in the vessel to liquid B being mixed = 1: 2
Since the quantity of liquid B being mixed is 20 liters, the quantity of liquid left in the vessel is 10 liters.
Therefore, the total quantity of liquid initially present in the vessel = 10 + 20 = 30 liters
Quantity of liquid A = 3 / (2 + 3) × 30 = 18 liters.
Correct Answer: 64 : 61
Explanation:
Here, quantity of wine left after third operation
= [1 - (5 / 25)]3 x 25 = (4 / 5)3 x 25 = (64 / 125) x 25 = (64 / 5) = 12 4/5 liters.
Final ratio of wine to water = (64 / 125) / (1- 64 /125)
= (64 / 125) /(61 / 125)
Wine : Water = (64 / 61)
Correct Answer: 72 kms
Explanation:
Average speed = (100 / 10) = 10 km/hr.
Ratio of time taken at 7 km/hr to 12 km/hr = 2 : 3
Time taken at 7 km/hr = 2 (2 + 3) × 10 = 4 hrs.
Distance covered at 7 km/hr = 7 × 4 = 28 km.
Distance covered at 12 km/hr = 100 ? 28 = 72 km.
Correct Answer: 4 kg
Explanation:
Correct Answer: 2 3
Explanation:
Correct Answer: Rs. 750
Explanation:
Correct Answer: 10 litre
Explanation:
Correct Answer: 13 litre 45
Explanation:
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