A mixture contains A and B in the ratio 5 : 7. 24 litres of this mixtu...
E) 35 litres Explanation: Total = 5x+7x+24 = 12x+24 So 5x+15/7x = 10/7 Solve, x = 3 So total = 12*3 + 24 = 60 litres So B = 7/(5+7) * 60 = 35
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A mixture contains A and B in the ratio 5 : 7. 24 litres of this mixtu...
Let's assume that the original amount of A in the mixture is 5x liters and the original amount of B is 7x liters.
24 liters of the mixture is taken out, so the remaining mixture will have (5x+7x-24) liters.
Then, 15 liters of A is poured in, so the new amount of A becomes (5x+15) liters.
The ratio of A to B in the new mixture is given as 10:7.
Therefore, we can set up the equation:
(5x+15)/(7x-24) = 10/7
Now, let's solve the equation to find the value of x.
Cross-multiplying the equation, we get:
7(5x+15) = 10(7x-24)
35x + 105 = 70x - 240
Simplifying the equation, we get:
35x - 70x = -240 - 105
-35x = -345
Dividing both sides of the equation by -35, we get:
x = 345/35
x ≈ 9.857
Since we are looking for the amount of B originally present in the mixture, we need to find the value of 7x.
7x = 7 * 9.857
7x ≈ 69
Therefore, the amount of B originally present in the mixture is approximately 69 liters.
Hence, the correct answer is option E: 35 liters.