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Answers
Answer:
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=x−27−
x
x−27
×15
Amount of water =27-\dfrac{27}{x}\times 15+15=27−
x
27
×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\%
Capacity of vessel
Amount of milk in mixture
×100=71.11%
\dfrac{(x-27)(x-15)}{x^2}\times 100=71.11
x
2
(x−27)(x−15)
×100=71.11
x^2-42x+405=0.7111x^2x
2
−42x+405=0.7111x
2
0.2889x^2-42x+405=00.2889x
2
−42x+405=0
x=\dfrac{42\pm\sqrt{42^2-4\times 405\times 0.2889}}{2\times 0.2889}x=
2×0.2889
42±
42
2
−4×405×0.2889
x\approx 135, x\approx 10.38x≈135,x≈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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