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A jar contains a mixture of two liquids A and B in the ratio 4 : 1. When 10 litres of the mixture is taken out and 10 litres of liquid B is poured into the jar, the ratio becomes 2 : 3. How many litres of liquid A was contained in the jar?
- a)14 litres
- b)18 litres
- c)20 litres
- d)16 litres
- e)None of these
Correct answer is option 'D'. 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...
Let the quantity of a and b is 4x and x
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A jar contains a mixture of two liquids A and B in the ratio 4 : 1. Wh...
Problem Analysis:
We are given a jar containing a mixture of two liquids A and B in the ratio 4:1. We have to find the quantity of liquid A in the jar.
Given Data:
Ratio of liquids A and B in the jar = 4:1
Quantity of mixture taken out = 10 litres
Quantity of liquid B poured into the jar = 10 litres
New ratio of liquids A and B in the jar = 2:3
Solution:
Let us assume that the initial quantity of liquid A in the jar was 4x litres and that of liquid B was x litres. Therefore, the total quantity of mixture in the jar was 5x litres.
As per the given data, when 10 litres of the mixture is taken out, the quantity of liquid A in the jar becomes 4x - (4/5) * 10 = 4x - 8 litres, and the quantity of liquid B becomes x - (1/5) * 10 = x - 2 litres.
Now, 10 litres of liquid B is poured into the jar. Therefore, the new quantity of liquid B in the jar becomes x - 2 + 10 = x + 8 litres.
According to the question, the new ratio of liquids A and B in the jar is 2:3. Therefore, we can write:
(4x - 8) : (x + 8) = 2 : 3
Cross-multiplying, we get:
6(4x - 8) = 2(x + 8)
24x - 48 = 2x + 16
22x = 64
x = 64/22 = 32/11
Substituting the value of x in the equation (4x - 8) : (x + 8) = 2 : 3, we get:
(4 * (32/11) - 8) : ((32/11) + 8) = 2 : 3
16/11 : (96/11) = 2 : 3
Multiplying both sides by 11, we get:
16 : 96 = 2 : 3
Therefore, the initial quantity of liquid A in the jar was 4x = 4 * (32/11) = 128/11 litres.
Therefore, the correct option is (d) 16 litres.
Final Answer:
The initial quantity of liquid A in the jar was 128/11 litres, which is approximately equal to 11.64 litres.
We are given a jar containing a mixture of two liquids A and B in the ratio 4:1. We have to find the quantity of liquid A in the jar.
Given Data:
Ratio of liquids A and B in the jar = 4:1
Quantity of mixture taken out = 10 litres
Quantity of liquid B poured into the jar = 10 litres
New ratio of liquids A and B in the jar = 2:3
Solution:
Let us assume that the initial quantity of liquid A in the jar was 4x litres and that of liquid B was x litres. Therefore, the total quantity of mixture in the jar was 5x litres.
As per the given data, when 10 litres of the mixture is taken out, the quantity of liquid A in the jar becomes 4x - (4/5) * 10 = 4x - 8 litres, and the quantity of liquid B becomes x - (1/5) * 10 = x - 2 litres.
Now, 10 litres of liquid B is poured into the jar. Therefore, the new quantity of liquid B in the jar becomes x - 2 + 10 = x + 8 litres.
According to the question, the new ratio of liquids A and B in the jar is 2:3. Therefore, we can write:
(4x - 8) : (x + 8) = 2 : 3
Cross-multiplying, we get:
6(4x - 8) = 2(x + 8)
24x - 48 = 2x + 16
22x = 64
x = 64/22 = 32/11
Substituting the value of x in the equation (4x - 8) : (x + 8) = 2 : 3, we get:
(4 * (32/11) - 8) : ((32/11) + 8) = 2 : 3
16/11 : (96/11) = 2 : 3
Multiplying both sides by 11, we get:
16 : 96 = 2 : 3
Therefore, the initial quantity of liquid A in the jar was 4x = 4 * (32/11) = 128/11 litres.
Therefore, the correct option is (d) 16 litres.
Final Answer:
The initial quantity of liquid A in the jar was 128/11 litres, which is approximately equal to 11.64 litres.
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