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1. The ratio, in which tea costing Rs. 192 per kg is to be mixed with tea costing Rs. 150 per kg so that the mixed tea when sold for Rs. 194.40 per kg, gives a profit of 20%.

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Solution:
CP of first tea = Rs. 192 per kg.
CP of Second tea = Rs. 150 per kg.
Mixture is to be sold in Rs. 194.40 per kg, which has included 20% profit. So,
SP of Mixture = Rs. 194.40 per kg.
Let the CP of Mixture be Rs. X per kg. Therefore,
X + 20% of X = SP
6X5 = 194.40
6X = 194.40 *5
X = Rs. 162 per kg.
Let N kg of first tea and M kg of second tea to be added.
Now, Using Alligation,
We get,
Alligation mcq Solution1
NM=1230
N : M = 2 : 5
2. An alloy contains zinc, copper and tin in the ratio 2 : 3 : 1 and another contains copper, tin and lead in the ratio 5 : 4 : 3. If equal weights of both alloys are melted together to form a third alloy, then the weight of lead per kg in new alloy will be:

Discuss
Solution:
Ratio of Zinc, Copper and Tin is given as,
Z : C : T = 2 : 3 : 1.
Now, let the first alloy be 12 kg (taken as 4 kg Zinc, 6 kg Copper and 2 Kg Lead).Weight of second alloy = 12 kg as, C : T : L = 5 : 4 : 3. (taken as 5 kg Copper, 4 kg Tin and 3 Kg Lead.)
Alloys are mixed together to form third alloy. Then the ratio of content in it,
Z : C : T : L = 4 : (6 + 5) : (2 + 4) : 3
Weight of third alloy = 12 + 12 = 24 Kg.
So, weight of the Lead = 324 = 18 kg.
3. In a 729 litres mixture of milk and water, the ratio of milk to water is 7 : 2. to get a new mixture containing milk and water in the ratio 7 : 3, the amount of water to be added is:

Discuss
Solution:
Quantity of milk in 729 litre of mixture
= 7 × 7299 = 567 litre
Quantity of water
= 729 - 567
= 162 litres
Let x litre of water be added to become ratio 7 : 3
Alligation mcq Solution 2
Or, 73 = 567162+x
Or, 162 × 7 + 7x = 567 × 3
Or, 7x = 1701 - 1134 = 567
Or, x = 5677 = 81 litres water is to be added.
4. In what ratio must a mixture of 30% alcohol strength be mixed with that of 50% alcohol strength so as to get a mixture of 45% alcohol strength?

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Solution:
Alligation mcq Solution2
5. To gain 10% on selling sample of milk at the cost price of pure milk, the quantity of water to be mixed with 50 kg. of pure milk is:

Discuss
Solution:

1st Method (Method of Alligation):
Let the quantity of water to be mixed is x kg.
Let cost of milk be Rs. 1 per kg.
Then SP of 50 kg of milk with gain 10% = Rs. 55 [As Cost of 50 kg milk = Rs. 50, then SP = (50 + 10% of 50)]
Alligation mcq Solution
Then, water to be mixed is 5 kg, As the selling price of the milk is Rs. 1 per kg. Seller has to have 10% gain on 50 kg milk, he must have to add 5 kg water to 50 kg milk.

2nd Method (Simple Method):
Let the quantity of water mixed be x kg.
Let CP of 1 kg of pure milk = Rs. 1.
Hence,
% gain = x × 10050
10 = 100x50
Or, 2x = 10
or, x = 5 kg.

6. From a container, full of pure milk, 20% is replaced by water and this process is repeated three times. At the end of third operation, the quantity of pure milk reduces to:

Discuss
Solution:
Let pure milk was 100L. So,
Water is replaced 20% in per process = 20% of 100 = 20L.
Now, we use short-cut formula for it.
Quantity of Milk reduced to,
=X×[1−YX]n=100×[1−20100]3=100×64125=51.2%

Here,
X = Initial quantity of milk.
Y = Replaced water in per process.
n = No. of process repeated.

Note:
The formula used in above problem is quite similar to depreciation formula or Compound interest formula.

Alternatively,
Let pure milk be 100 litres initially.
After third operation, milk will be
100 == 20%↓(- 20L) ⇒ 80 == 20%↓(- 16L) ⇒ 64 == 20%↓(-12.8L) ⇒ 51.2 %
7. Three types of wheat of Rs. 1.27, Rs. 1.29 and Rs. 1.32 per kg are mixed together to be sold at Rs. 1.30 per kg. In what ratio should this wheat be mixed?

Discuss
Solution:
Average cost: Rs. 1.30 per kg.
Alligation mcq solution image
And,
Alligation mcq solution image
Hence, ratio of 1.27, 1.29 and 1.32
⇒ n1 : n2 : n3 = 2 : (2 × 3) : 3
⇒ n1 : n2 : n3 = 2 : 6 : 3
8. In a zoo, there are deers and ducks. If the heads are counted, there are 180, while the legs are 448. What will be the number of deers in the zoo?

Discuss
Solution:
Average legs per head = 448180
Alligation mcq Solution
Deers : Ducks = 88 : 272
Hence, the number of Deers = 180×88360   = 44
9. An amount of Rs. 680 was invested at 6% rate of interest and another sum of money was invested at 10% interest. If the average interest on the total at the end of the year was 7.5%, how much was invested at 10%?

Discuss
Solution:
Alligation mcq Solution 7
Now, 680x=2.51.5
Or, x=680×35
Hence, x = Rs. 408
10. A trader has 50 kg of pulses, part of which he sells at 14% profit and rest at 6% loss. On the whole his loss is 4%. How much quantity is sold at 14% profit and that at 6% loss?

Discuss
Solution:
Alligation mcq Solution 8
Hence, ratio of quantity sold at 14% profit and 6% loss,
= 2 : 18 = 1 : 9
Hence, pulses sold at 14% profit,
= 50×110  = 5 kg.
At 6% Wheat sold at loss = 45 kg.

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