Question:
A shopkeeper has two jars P and Q containing almond oil in the ratio 2 : 3 respectively. He mixes '3x' litres and '2x' litres of olive oil in P and Q, respectively, after which the percentage of olive oil in jar P becomes 80% more than that in jar Q. If mixtures from jar P and jar Q are then mixed in the ratio of 3 : 1, what will be the percentage of olive oil in the resultant mixture?
A shopkeeper has two jars P and Q containing almond oil in the ratio 2 : 3 respectively. He mixes '3x' litres and '2x' litres of olive oil in P and Q, respectively, after which the percentage of olive oil in jar P becomes 80% more than that in jar Q. If mixtures from jar P and jar Q are then mixed in the ratio of 3 : 1, what will be the percentage of olive oil in the resultant mixture?
Updated On: Sep 13, 2024
- 45%
- 44%
- 66%
- 32%
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The Correct Option is D
Solution and Explanation
The correct option is (D): 32%.
Let the almond oil in P = 2a and in Q = 3a
\(\frac{3x}{(2a + 3x)}\) : \(\frac{2x}{(3a + 2x)}\) = 180 : 100
(3a + 2x) : (2a + 3x) = 6 : 5
a : x = 8 : 3
In P, Olive oil/Mixture = \(\frac{3x}{(2a + 3x)}\) =\(\frac{ 9}{25}\) => 36%
In Q, Olive oil/Mixture = \(\frac{2x}{(3a + 2x)}\)= \(\frac{ 6}{30}\) => 20%
Percentage of Olive oil in the final mixture = (3 * 36% + 1 * 20%)/(3 +1) = 32%
Let the almond oil in P = 2a and in Q = 3a
\(\frac{3x}{(2a + 3x)}\) : \(\frac{2x}{(3a + 2x)}\) = 180 : 100
(3a + 2x) : (2a + 3x) = 6 : 5
a : x = 8 : 3
In P, Olive oil/Mixture = \(\frac{3x}{(2a + 3x)}\) =\(\frac{ 9}{25}\) => 36%
In Q, Olive oil/Mixture = \(\frac{2x}{(3a + 2x)}\)= \(\frac{ 6}{30}\) => 20%
Percentage of Olive oil in the final mixture = (3 * 36% + 1 * 20%)/(3 +1) = 32%
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