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8 litres are drawn from a flask containing milk and then filled with water. The operation is performed 3 more times. The ratio of the quantity of milk left and total solution is 81/625. How much milk the flask initially holds?
- a)10ltr
- b)20ltr
- c)30ltr
- d)40ltr
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
8 litres are drawn from a flask containing milk and then filled with w...
Answer – b) 20ltr Explanation : let initial quantity be Q, and final quantity be F F = Q*(1 – 8/Q)^4
81/625 = (1-8/Q)^4
3/5 = 1 – 8/Q
Q = 20
81/625 = (1-8/Q)^4
3/5 = 1 – 8/Q
Q = 20
Most Upvoted Answer
8 litres are drawn from a flask containing milk and then filled with w...
Let's assume that the initial quantity of milk in the flask is 'x' liters.
After drawing out 8 liters from the flask, the quantity of milk left in the flask will be (x - 8) liters. At the same time, the quantity of the solution in the flask will be (x - 8 + 8) liters, which is equal to x liters.
Now, the operation is performed 3 more times. Each time, 8 liters are drawn out and replaced with water. So, after the first operation, the quantity of milk left in the flask is (x - 8) liters and the quantity of the solution is x liters. After the second operation, the quantity of milk left in the flask is [(x - 8) - 8] liters and the quantity of the solution is [x + 8] liters. After the third operation, the quantity of milk left in the flask is [((x - 8) - 8) - 8] liters and the quantity of the solution is [(x + 8) + 8] liters. And after the fourth operation, the quantity of milk left in the flask is [[(((x - 8) - 8) - 8) - 8] liters and the quantity of the solution is [((x + 8) + 8) + 8] liters.
According to the given information, the ratio of the quantity of milk left to the total solution is 81/625. Therefore,
[(x - 8 - 8 - 8 - 8) / (((x + 8) + 8) + 8)] = 81/625
Simplifying this equation, we get:
[(x - 32) / (x + 24)] = 81/625
Cross-multiplying, we get:
625(x - 32) = 81(x + 24)
625x - 20000 = 81x + 1944
544x = 21944
x = 40
Therefore, the flask initially holds 40 liters of milk, which is option (B).
After drawing out 8 liters from the flask, the quantity of milk left in the flask will be (x - 8) liters. At the same time, the quantity of the solution in the flask will be (x - 8 + 8) liters, which is equal to x liters.
Now, the operation is performed 3 more times. Each time, 8 liters are drawn out and replaced with water. So, after the first operation, the quantity of milk left in the flask is (x - 8) liters and the quantity of the solution is x liters. After the second operation, the quantity of milk left in the flask is [(x - 8) - 8] liters and the quantity of the solution is [x + 8] liters. After the third operation, the quantity of milk left in the flask is [((x - 8) - 8) - 8] liters and the quantity of the solution is [(x + 8) + 8] liters. And after the fourth operation, the quantity of milk left in the flask is [[(((x - 8) - 8) - 8) - 8] liters and the quantity of the solution is [((x + 8) + 8) + 8] liters.
According to the given information, the ratio of the quantity of milk left to the total solution is 81/625. Therefore,
[(x - 8 - 8 - 8 - 8) / (((x + 8) + 8) + 8)] = 81/625
Simplifying this equation, we get:
[(x - 32) / (x + 24)] = 81/625
Cross-multiplying, we get:
625(x - 32) = 81(x + 24)
625x - 20000 = 81x + 1944
544x = 21944
x = 40
Therefore, the flask initially holds 40 liters of milk, which is option (B).
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