Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be:
A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5?
Milk in 1 litre mixture in 1st can = 3/4 litre.
Milk in 1 litre mixture in 2n d can = 1/2 litre.
Milk in 1 litre final mixture = 5/8 litre.
By rule of alligation we have required ratio 5 : 8
3/4 1/2
\ /
(5/8)
/ \
1/8 : 1/8
Therefore ratio of two mixtures =1/8:1/8=1:1
So, quantity of mixture taken from each can =(1/2)*12= 6 litres
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How many litres of water should be added to a 30 litre mixture of milk and water containing milk and water in the ratio of 7 : 3 such that the resultant mixture has 40% water in it?
30 litres of the mixture has milk and water in the ratio 7 : 3. i.e. the solution has 21 litres of milk
and 9 litres of water.
When you add more water, the amount of milk in the mixture remains constant at 21 litres. In the
first case, before addition of further water, 21 litres of milk accounts for 70% by volume. After
water is added, the new mixture contains 60% milk and 40% water.
Therefore, the 21 litres of milk accounts for 60% by volume.
Hence, 100% volume =21/0.6 = 35 litres.
We started with 30 litres and ended up with 35 litres.
So, 5 litres of water was added.
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A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2. 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more. At the end of the two removal and replacement, what is the ratio of milk and water in the resultant mixture?
The 20 litre mixture contains milk and water in the ratio of 3 : 2. Therefore, there will be 12 litres of milk in the mixture and 8 litres of water in the mixture.
Step 1: When 10 litres of the mixture is removed, 6 litres of milk is removed and 4 litres of water
is removed. Therefore, there will be 6 litres of milk and 4 litres of water left in the container. It is
then replaced with pure milk of 10 litres. Now the container will have 16 litres of milk and 4 litres
of water.
Step 2: When 10 litres of the new mixture is removed, 8 litres of milk and 2 litres of water is
removed. The container will have 8 litres of milk and 2 litres of water in it. Now 10 litres of pure
milk is added. Therefore, the container will have 18 litres of milk and 2 litres of water in it at the
end of the second step.
So, the ratio of milk and water is 18 : 2 or 9 : 1.
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Two vessels A and B contain spirit and water mixed in the ratio 5:2 and 7:6 respectively. Find the ratio in which these mixture be mixed to obtain a new mixture in vessel c containing spirit and water in the ratio 8:5?
Let's assume C.P. of spirit = Re. 1 per litre.
Spirit in 1 litre mix. of A = 5/7 litre. So C.P of 1 litre mix in A = Re. 5/7.
Spirit in 1 litre mix. of B = 7/13 litre. So C.P of 1 litre mix in B = Re. 7/13.
Spirit in 1-litre mix. of C = 8/13 litre. So C.P. of 1 litre mix in C = Re. 8/13.
By rule of an allegation, we have required ratio X:Y.
(5/7) (7/13)
\ /
(8/13)
/ \
(1/13) (9/91)
So, required ratio = 1/13 : 9/91 = 7:9.
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A coffee seller has two types of coffee Brand A costing 5 bits per pound and Brand B costing 3 bits per pound. He mixes two brands to get a 40 pound mixture. he sold this at 6 bits per pound. the seller gets a profit of 33 1/2 percent. how much he has used Brand A in the mixture?
Let x and y quantities of A and B respectively are mixed.
=> x+y=40 --------- (1)
His total selling price = 40*6=240
His cost price 180 approx(as he makes 33.5 % profit)
5x+3y=180 ------------- (2)
On solving (1) and (2)
x=30 pounds.
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In what ratio must water be added to 10 liters of milk at Rs.20 per liter so that cost of mixture is Rs.16 per liter?
10 lit milk cost 20 Rs For 1Rs, Milk = 1/2 lit
For 16Rs, Milk = (1/2)*16 = 8 lit (Milk)
Total quantity should be 10 litres.
so 10 - 8 = 2 lit ( water have to add)
Now ratio = 2(water) : 8(Milk) = 1:4
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A 10 Liter mixture of milk and water contains 30 percent water. Two liters of this mixture is taken away. How many liters of water should now be added so that the amount of milk in the mixture is double that of water?
Two liters were taken away So we have the only 8L of the mixture.
Amount of milk in 8 L of mixture = 8 * 70% = 5.6 liters
Amount of water in 8 L of mix = (8 - 5.6) = 2.4 L.
Half of milk i.e half of 5.6 = 2.8 L.
We need (2.8 - 2.4)L water more = 0.4 L
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An alloy of zinc and copper contains the metals in the ratio 5 : 3. The quantity of zinc to be added to 16 kg of the alloy so that the ratio of the metal may be 3 : 1 is:
Lets assume quantity of zinc to added = x kg.
zinc quantity in alloy = 5/8*16=10 Kg.
and copper quantity = 3/8*16=6 kg.
Alloy new ratio of zinc and copper = 3:1
Zinc quantity in alloy => (10+x)/6=3/1 => 10 + x = 18 => x = 8 kg.
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A certain quantity of 40% solution is replaced with 25% solution such that the new concentration is 35%. What is the fraction of the solution that was replaced?
Consider a solution = 1 ltr
X is the certain quantity which has to be replaced
Now,
40%of (1-x)+(25%of x)=35/100
=> 40/100 * (1-x) + 25x/100 = 35/100
=> 40/100 - 40x/100 + 25x/100 = 35/100
=> 15x/100 = 5/100
=> x = 1/3
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