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A mixture contains A and B in the ratio 5 : 9. 14 litres of this mixture is taken out and 14 litres of B is poured in. Now the ratio of A to B becomes 2 : 5. Find the amount of B originally present in the mixture.
- a)25 litres
- b)45 litres
- c)55 litres
- d)40 litres
- e)35 litres
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A mixture contains A and B in the ratio 5 : 9. 14 litres of this mixtu...
B) 45 litres Explanation: Total = 5x+9x+14 = 14x+14 So 5x/9x+14 = 2/5 Solve, x = 4 So total = 14*4 + 14 = 70 litres So B = 9/(5+9) * 70 = 45
Most Upvoted Answer
A mixture contains A and B in the ratio 5 : 9. 14 litres of this mixtu...
Given information:
- The initial ratio of A to B in the mixture is 5:9.
- 14 litres of the mixture is taken out, which means the amount of A and B both reduces by a certain proportion.
- 14 litres of B is added, which means the amount of B increases by 14 litres while the amount of A remains the same.
- The new ratio of A to B after the above operation is 2:5.
Let's solve the problem step by step:
Step 1: Find the initial amount of A and B in the mixture.
- Let the initial amount of the mixture be 5x + 9x = 14x (since the ratio of A to B is 5:9)
- Therefore, the initial amount of A in the mixture would be 5x and the initial amount of B would be 9x.
Step 2: Find the amount of A and B in the mixture after 14 litres is taken out.
- Since 14 litres is taken out, the new amount of the mixture would be 14x - 14 litres.
- Let the amount of A and B in the new mixture be a and b respectively.
- Since the amount of A and B in the mixture reduces in the same proportion, we can say that (5x - a) / (9x - b) = 14x / (14x - 14)
- Simplifying this equation, we get (5x - a) / (9x - b) = 5/8
Step 3: Find the amount of A and B in the mixture after 14 litres of B is added.
- After adding 14 litres of B, the new amount of B in the mixture would be 9x + 14 litres.
- Let the new amount of B in the mixture be y.
- Since the amount of A in the mixture remains the same, we can say that a / y = 2/5
- Simplifying this equation, we get y = (5a) / 2
Step 4: Solve for a and b.
- Using the equation from Step 2, we can say that (5x - a) / (9x - b) = 5/8
- Substituting y = (5a) / 2, we get (5x - a) / (9x - (2y/5)) = 5/8
- Simplifying this equation, we get 40x - 8a = 45y - 9y
- Substituting y = (5a) / 2, we get 40x - 8a = 225a / 2
- Simplifying this equation, we get a = (320x) / 41
- Substituting a in the equation y = (5a) / 2, we get y = (800x) / 41
- Using the equation for the initial amount of B (9x), we can say that 9x - b = 14 - (y - 9x)
- Substituting the values of y and a, we get b = (545x) / 41
Step 5: Find the initial amount of B.
- Using the value of b, we can say that the initial amount of B in the mixture is 545x
- The initial ratio of A to B in the mixture is 5:9.
- 14 litres of the mixture is taken out, which means the amount of A and B both reduces by a certain proportion.
- 14 litres of B is added, which means the amount of B increases by 14 litres while the amount of A remains the same.
- The new ratio of A to B after the above operation is 2:5.
Let's solve the problem step by step:
Step 1: Find the initial amount of A and B in the mixture.
- Let the initial amount of the mixture be 5x + 9x = 14x (since the ratio of A to B is 5:9)
- Therefore, the initial amount of A in the mixture would be 5x and the initial amount of B would be 9x.
Step 2: Find the amount of A and B in the mixture after 14 litres is taken out.
- Since 14 litres is taken out, the new amount of the mixture would be 14x - 14 litres.
- Let the amount of A and B in the new mixture be a and b respectively.
- Since the amount of A and B in the mixture reduces in the same proportion, we can say that (5x - a) / (9x - b) = 14x / (14x - 14)
- Simplifying this equation, we get (5x - a) / (9x - b) = 5/8
Step 3: Find the amount of A and B in the mixture after 14 litres of B is added.
- After adding 14 litres of B, the new amount of B in the mixture would be 9x + 14 litres.
- Let the new amount of B in the mixture be y.
- Since the amount of A in the mixture remains the same, we can say that a / y = 2/5
- Simplifying this equation, we get y = (5a) / 2
Step 4: Solve for a and b.
- Using the equation from Step 2, we can say that (5x - a) / (9x - b) = 5/8
- Substituting y = (5a) / 2, we get (5x - a) / (9x - (2y/5)) = 5/8
- Simplifying this equation, we get 40x - 8a = 45y - 9y
- Substituting y = (5a) / 2, we get 40x - 8a = 225a / 2
- Simplifying this equation, we get a = (320x) / 41
- Substituting a in the equation y = (5a) / 2, we get y = (800x) / 41
- Using the equation for the initial amount of B (9x), we can say that 9x - b = 14 - (y - 9x)
- Substituting the values of y and a, we get b = (545x) / 41
Step 5: Find the initial amount of B.
- Using the value of b, we can say that the initial amount of B in the mixture is 545x
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A mixture contains A and B in the ratio 5 : 9. 14 litres of this mixture is taken out and 14 litres of B is poured in. Now the ratio of A to B becomes 2 : 5. Find the amount of B originally present in the mixture.a)25 litresb)45 litresc)55 litresd)40 litrese)35 litresCorrect answer is option 'B'. Can you explain this answer?
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A mixture contains A and B in the ratio 5 : 9. 14 litres of this mixture is taken out and 14 litres of B is poured in. Now the ratio of A to B becomes 2 : 5. Find the amount of B originally present in the mixture.a)25 litresb)45 litresc)55 litresd)40 litrese)35 litresCorrect answer is option 'B'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A mixture contains A and B in the ratio 5 : 9. 14 litres of this mixture is taken out and 14 litres of B is poured in. Now the ratio of A to B becomes 2 : 5. Find the amount of B originally present in the mixture.a)25 litresb)45 litresc)55 litresd)40 litrese)35 litresCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A mixture contains A and B in the ratio 5 : 9. 14 litres of this mixture is taken out and 14 litres of B is poured in. Now the ratio of A to B becomes 2 : 5. Find the amount of B originally present in the mixture.a)25 litresb)45 litresc)55 litresd)40 litrese)35 litresCorrect answer is option 'B'. Can you explain this answer?.
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