MIXTURE & ALLIGATION
- Two equal glasses of the same type are respectively 1/3 and 1/4 full of milk. They are then filled up with water and the contents are mixed in a pot. What is the ratio of milk and water in the pot ?(2015)
(A) 7:17
(B) 1:3
(C) 9:21
(D) 11:23
Answer-A
Let's assume each glass has a capacity of x units.
The first glass is 1/3 full of milk, which means it contains (1/3) * x = x/3 units of milk. The remaining 2/3 of the glass is filled with water, which is (2/3) * x = 2x/3 units of water.
The second glass is 1/4 full of milk, which means it contains (1/4) * x = x/4 units of milk. The remaining 3/4 of the glass is filled with water, which is (3/4) * x = 3x/4 units of water.
When the contents of both glasses are mixed in a pot, we add the amounts of milk and water together.
Milk: (x/3) + (x/4) = (4x + 3x) / 12 = 7x / 12
Water: (2x/3) + (3x/4) = (8x + 9x) / 12 = 17x / 12
The ratio of milk to water in the pot is (7x / 12) : (17x / 12), which simplifies to 7x : 17x.
Since the ratio is in terms of x, we can conclude that the ratio of milk to water in the pot is always 7:17, regardless of the value of x.
Therefore, the correct answer is (a) 7:17.
- 30 g of sugar was mixed in 180 ml water in a vessel A, 40 g of sugar was mixed in 280 ml of water in vessel B and 20 g of sugar was mixed in 100 ml of water in vessel C. The solution in vessel B is (2016)
(A) sweeter than that in C
(B) sweeter than that in A
(C) as sweet as that in C
(D) less sweet than that in C
Answer-D
To determine the sweetness of the solutions in vessels A, B, and C, we can compare the ratios of sugar to water in each vessel.
In vessel A, the ratio of sugar to water is 30 g : 180 ml = 1 g : 6 ml.
In vessel B, the ratio of sugar to water is 40 g : 280 ml = 1 g : 7 ml.
In vessel C, the ratio of sugar to water is 20 g : 100 ml = 1 g : 5 ml.
Comparing the ratios, we can conclude that the solution in vessel B is less sweet than the solution in vessel C.
Hence, the correct answer is (d) less sweet than that in C.
- There is a milk sample with 50% water in it. If 1/3rd of this milk is added to equal amount of pure milk, then water in the new mixture will fall down to (2017)
(A) 25%
(B) 30%
(C) 35%
(D) 40%
Answer-A
Let's assume that we have 1 liter of the milk sample with 50% water, which means it has 500 ml of water and 500 ml of milk.
If we take 1/3rd of this milk, it will be (1/3) * 1 liter = 333.33 ml of the milk sample. This 333.33 ml of the milk sample will have (1/2) * 333.33 ml = 166.67 ml of water and (1/2) * 333.33 ml = 166.67 ml of milk.
Now, if we add this 333.33 ml of the milk sample to an equal amount of pure milk (i.e., 333.33 ml), the resulting mixture will have a total of 666.66 ml of milk, out of which 166.67 ml is water and 500 ml is milk.
Thus, the ratio of water to milk in the resulting mixture will be 166.67 ml : 500 ml, which simplifies to 1 : 3.
Therefore, the percentage of water in the resulting mixture will be (1 / (1 + 3)) * 100% = 25%.
Hence, the correct answer is (a) 25%.
- A bottle contains 20 litres of liquid A. 4 litres of liquid A is taken out of it and replaced by same quantity of liquid B. Again 4 litres of the mixture is taken out and replaced by same quantity of liquid B. What is the ratio of quantity of liquid A to that of liquid B in the final mixture?(2020)
(A) 4: 1
(B) 5: 1
(C) 16 : 9
(D) 17: 8
Answer-C
Let's calculate the quantity of liquid A and liquid B at each step to determine the final ratio.
Step 1:
Initially, the bottle contains 20 litres of liquid A. 4 litres of liquid A is taken out and replaced with an equal quantity of liquid B.
Liquid A after Step 1: 20 - 4 = 16 liters
Liquid B after Step 1: 4 liters
Step 2:
Now, 4 litres of the mixture (which consists of 16 liters of liquid A and 4 liters of liquid B) is taken out and replaced with an equal quantity of liquid B.
Liquid A after Step 2: 16 - (4/20) * 16 = 16 - 3.2 = 12.8 liters
Liquid B after Step 2: 4 + 3.2 = 7.2 liters
Therefore, the ratio of liquid A to liquid B in the final mixture is:
Liquid A: Liquid B = 12.8 liters : 7.2 liters
Simplifying the ratio by dividing both sides by 0.8 (the common factor):
Liquid A: Liquid B = 16 liters : 9 liters
- There are two containers X and Y. X contains 100 ml of milk and Y contains 100 ml of water. 20 ml of milk from X is transferred to Y. After mixing well, 20 ml of the mixture in Y is transferred back to X. If m denotes the proportion of milk in X and n denotes the proportion of water in Y, then which one of the following is correct?(2022)
(A) m= n
(B) m>n
(C) m<n
(D) Cannot be determined due to insufficient data
Answer-A
Let's calculate the proportions of milk in container X (m) and water in container Y (n) after the given operations.
Initially:
Container X: 100 ml of milk
Container Y: 100 ml of water
Step 1:
20 ml of milk from container X is transferred to container Y.
Container X: 100 ml - 20 ml = 80 ml of milk
Container Y: 100 ml + 20 ml = 120 ml of water
Step 2:
20 ml of the mixture in container Y (which consists of 100 ml of water and 20 ml of milk) is transferred back to container X.
Container X: 80 ml + 20 ml = 100 ml of milk
Container Y: 120 ml - 20 ml = 100 ml of water
After the operations, we have:
Container X: 100 ml of milk
Container Y: 100 ml of water
Now, let's calculate the proportions m and n:
m = (amount of milk in container X) / (total volume of container X)
= 100 ml / 100 ml
= 1
n = (amount of water in container Y) / (total volume of container Y)
= 100 ml / 100 ml
= 1
Therefore, we find that m = n, which means the correct option is (a) m = n.
