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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...
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A jar contains a mixture of two liquids A and B in the ratio 4 : 1. Wh...
Given:
- The ratio of liquids A and B in the jar is 4:1.
- When 10 litres of the mixture is taken out and 10 litres of liquid B is poured in, the new ratio becomes 2:3.
To find:
- How many litres of liquid A was contained in the jar initially.
Solution:
Let's assume the initial volume of the mixture in the jar is 4x litres of liquid A and x litres of liquid B.
Step 1: Calculation before removing 10 litres and adding 10 litres of B
- The total volume of the mixture in the jar initially = 4x + x = 5x litres.
- The ratio of A to B in the jar initially = 4x : x = 4 : 1.
Step 2: Calculation after removing 10 litres and adding 10 litres of B
- 10 litres of the mixture is taken out, so the remaining volume of the mixture = 5x - 10 litres.
- 10 litres of liquid B is poured into the jar, so the final volume of liquid B = x + 10 litres.
- The new ratio of A to B in the jar = 4x : (x + 10) = 2 : 3.
Step 3: Solving the equation
- Cross-multiplying the ratio equation, we get 2(x + 10) = 3(4x).
- Simplifying the equation, we have 2x + 20 = 12x.
- Subtracting 2x from both sides, we get 20 = 10x.
- Dividing both sides by 10, we get x = 2.
Step 4: Calculation of liquid A
- Substituting the value of x in the initial volume equation, we have 4x = 4 * 2 = 8 litres.
- Therefore, the initial volume of liquid A in the jar was 8 litres.
Hence, the correct answer is option D) 16 litres.
- The ratio of liquids A and B in the jar is 4:1.
- When 10 litres of the mixture is taken out and 10 litres of liquid B is poured in, the new ratio becomes 2:3.
To find:
- How many litres of liquid A was contained in the jar initially.
Solution:
Let's assume the initial volume of the mixture in the jar is 4x litres of liquid A and x litres of liquid B.
Step 1: Calculation before removing 10 litres and adding 10 litres of B
- The total volume of the mixture in the jar initially = 4x + x = 5x litres.
- The ratio of A to B in the jar initially = 4x : x = 4 : 1.
Step 2: Calculation after removing 10 litres and adding 10 litres of B
- 10 litres of the mixture is taken out, so the remaining volume of the mixture = 5x - 10 litres.
- 10 litres of liquid B is poured into the jar, so the final volume of liquid B = x + 10 litres.
- The new ratio of A to B in the jar = 4x : (x + 10) = 2 : 3.
Step 3: Solving the equation
- Cross-multiplying the ratio equation, we get 2(x + 10) = 3(4x).
- Simplifying the equation, we have 2x + 20 = 12x.
- Subtracting 2x from both sides, we get 20 = 10x.
- Dividing both sides by 10, we get x = 2.
Step 4: Calculation of liquid A
- Substituting the value of x in the initial volume equation, we have 4x = 4 * 2 = 8 litres.
- Therefore, the initial volume of liquid A in the jar was 8 litres.
Hence, the correct answer is option D) 16 litres.
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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 litresb)18 litresc)20 litresd)16 litrese)None of theseCorrect answer is option 'D'. Can you explain this answer?
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