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A jar contains a mixture of two liquids A and B in the ratio 4 : 1. When 10 liter of the mixture is replaced with liquid B, the ratio becomes 2 : 3. The volume of liquid A present in the jar earlier was ______ liters.
Correct answer is '16'. Can you explain this answer?
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A jar contains a mixture of two liquids A and B in the ratio 4 : 1. Wh...
Given
Jar contains a mixture of two liquids A and B in the ratio 4 : 1
Volume of liquid A =4x liters
Volume of liquid B= x liters
∴ Total volume of mixture = 4x + x = 5x liters
∴ 10 liter of the mixture is removed.
∴ Volume of liquid A removed =(4/5)x10 liters = 8 liters
Volume of liquid B removed = (1/5)x10 liters = 2 liters
Again, 10 liter of liquid B is added in place of 10 liters liquid
∴ Volume of liquid A in new mixture = (4x-8) liters
Volume of liquid B in new mixture =(x-2+10) liters = (x+8) liters
According to the question,
⇒3(4x - 8) = 2(x+8)
⇒12x - 24 = 2x + 16
⇒10x = 40
⇒x = 4
∴ Volume of A in earlier mixture = 4x4 liters = 16 liters
Hence, the volume of present in the jar earlier was 16 liters.
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A jar contains a mixture of two liquids A and B in the ratio 4 : 1. Wh...
Problem:
A jar contains a mixture of two liquids A and B in the ratio 4 : 1. When 10 liters of the mixture is replaced with liquid B, the ratio becomes 2 : 3. The volume of liquid A present in the jar earlier was ______ liters.

Solution:
Let's solve this problem step by step:

Step 1: Setting up the equation
Let's assume the initial volume of the mixture in the jar is x liters. Since the ratio of liquid A to liquid B is 4:1, the volume of liquid A would be (4/5)x liters and the volume of liquid B would be (1/5)x liters.

Step 2: Volume of liquid A after replacement
When 10 liters of the mixture is replaced with liquid B, the volume of liquid B becomes ((1/5)x + 10) liters. Since the ratio of liquid A to liquid B becomes 2:3, the volume of liquid A would be (2/5) of the total volume, which is ((2/5)x + 2/5*10) liters.

Step 3: Equating the volumes of liquid A
Equating the volume of liquid A before and after the replacement, we get:

(4/5)x = (2/5)x + 2/5*10

Simplifying this equation, we get:

(4/5)x - (2/5)x = 4

(2/5)x = 4

Multiplying both sides by 5/2, we get:

x = 4 * (5/2)

x = 20/2

x = 10

Step 4: Finding the volume of liquid A
Now that we know the initial volume of the mixture in the jar is 10 liters, we can calculate the volume of liquid A:

Volume of liquid A = (4/5) * 10

Volume of liquid A = 40/5

Volume of liquid A = 8 liters

Therefore, the volume of liquid A present in the jar earlier was 8 liters.
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A jar contains a mixture of two liquids A and B in the ratio 4 : 1. When 10 liter of the mixture is replaced with liquid B, the ratio becomes 2 : 3. The volume of liquid A present in the jar earlier was ______ liters.Correct answer is '16'. Can you explain this answer?
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