Two matching pitchers contain grapefruit juice. Pitcher A is 1/3 full. Pitcher B is 2/5 full. Each pitcher is then filled with water. The contents of both pitchers are poured into one large bowl. What fraction of the liquid is grapefruit juice?
The fraction of the liquid in large container is grapefruit juice \(\frac{11}{15}\) .
A mixture, as the name suggests is mixing two or more things together and alligation enables us to find the ratio in which the ingredients/ things have been mixed and at what price they are sole to earn profit or face loss.
According to the question
Pitcher A is 1/3 full with grapefruit juice
and rest is Pitcher A is 2/3 full with water .
Pitcher B is 2/5 full with grapefruit juice
and rest is Pitcher B is 3/5 full with water .
Now,
The contents of both pitchers are poured into one large bowl
Therefore fraction of the liquid is grapefruit juice is
= fraction of grapefruit juice in pitcher A + fraction of grapefruit juice in pitcher B
= \(\frac{1}{3} + \frac{2}{5}\)
= \(\frac{5+6}{15}\)
= \(\frac{11}{15}\)
Hence, the fraction of the liquid is grapefruit juice is \(\frac{11}{15}\) .
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