Question

1. A vessel is completely filled with milk. 27
litres of milk is taken out and replaced by
water. Again 15 ltr of mixture is taken out
and vessel is filled with water again. Now
concentration of milk in the mixture
becomes 71.11%. What is the capacity of
container?
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Answer 1

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Answer 2

The capacity of container is 135 liters

Step-by-step explanation:

Let the capacity of vessel filled with milk be x lt

Case 1: First 27 lt of milk is taken out and replaced by water

Amount of milk = x - 27

Amount of water = 27

Case 2: Again 15 lt of mixture is taken out and filled with water.

Amount of milk $=x-27-\dfrac{x-27}{x}\times 15$

Amount of water $=27-\dfrac{27}{x}\times 15+15$

Now concentration of milk in the mixture becomes 72.11%

$\dfrac{\text{Amount of milk in mixture}}{\text{Capacity of vessel}}\times 100=71.11\%$

$\dfrac{(x-27)(x-15)}{x^2}\times 100=71.11$

$x^2-42x+405=0.7111x^2$

$0.2889x^2-42x+405=0$

$x=\dfrac{42\pm\sqrt{42^2-4\times 405\times 0.2889}}{2\times 0.2889}$

$x\approx 135, x\approx 10.38$

10.38 is not possible because taken out milk was 27 lt.

Hence, the capacity of container is 135 liters

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