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Two casks A and B are filled with two kinds of liquids. First and Second kind of liquids mixed in cask A in the ratio 2:7 and in cask B in the ratio 1:5 respectively. What quantity must be taken from each cask to form a mixture which shall consist of 2 litres of First Liquid and 9 litres of Second Liquid?
- a)4:7
- b)3:8
- c)5:6
- d)1:10
- e)2:1
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Two casks A and B are filled with two kinds of liquids. First and Sec...
Total mixture required = 2 + 9 = 11 litres
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Let 'x' litres be taken from the first cask. Then the mixture taken from the second cask = (11 - x) litres
Quantity of first kind liquid in 'x' litres taken from the first cask = 2/9 * x
Quantity of first kind liquid in (11 - x) litres taken from the second cask = 1/6 * (11 - x)
Now, 2x/9 + 1/6 (11 - x) = 2
(4x + 33 - 3x)/18 = 2
x + 33 = 36
x = 3
The mixture taken from first cask = 3 litres
The mixture taken from second cask = (11 - x) = 8 litres
Thus the ratio is 3:8
Hence the correct answer is option B.
Most Upvoted Answer
Two casks A and B are filled with two kinds of liquids. First and Sec...
To solve this problem, we can set up a system of equations based on the given information and then solve for the quantities to be taken from each cask.
Let's assume that x litres of the first liquid are taken from cask A and y litres of the second liquid are taken from cask B.
The ratio of the first liquid in cask A is 2:7, so the fraction of the first liquid in the mixture taken from cask A is 2/(2+7) = 2/9. Therefore, the quantity of the first liquid in the mixture taken from cask A is (2/9)*x.
Similarly, the ratio of the second liquid in cask B is 1:5, so the fraction of the second liquid in the mixture taken from cask B is 5/(1+5) = 5/6. Therefore, the quantity of the second liquid in the mixture taken from cask B is (5/6)*y.
Since we want the mixture to consist of 2 litres of the first liquid and 9 litres of the second liquid, we can set up the following equations:
(2/9)*x + (5/6)*y = 2
(7/9)*x + (1/6)*y = 9
To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution:
From the first equation, we can express x in terms of y:
x = (18/2)*(2 - (5/6)*y)
Substituting this expression for x into the second equation, we get:
(7/9)*((18/2)*(2 - (5/6)*y)) + (1/6)*y = 9
Simplifying this equation will give us the value of y. Once we have y, we can substitute it back into the expression for x to find its value.
After solving the above equation, we get y = 24/5.
So, the quantity to be taken from cask A is:
x = (18/2)*(2 - (5/6)*(24/5)) = 24/5
Therefore, the ratio of the quantities to be taken from cask A and cask B is 24/5 : 24/5 = 1 : 1.
Hence, the correct answer is option B) 1:1.
Let's assume that x litres of the first liquid are taken from cask A and y litres of the second liquid are taken from cask B.
The ratio of the first liquid in cask A is 2:7, so the fraction of the first liquid in the mixture taken from cask A is 2/(2+7) = 2/9. Therefore, the quantity of the first liquid in the mixture taken from cask A is (2/9)*x.
Similarly, the ratio of the second liquid in cask B is 1:5, so the fraction of the second liquid in the mixture taken from cask B is 5/(1+5) = 5/6. Therefore, the quantity of the second liquid in the mixture taken from cask B is (5/6)*y.
Since we want the mixture to consist of 2 litres of the first liquid and 9 litres of the second liquid, we can set up the following equations:
(2/9)*x + (5/6)*y = 2
(7/9)*x + (1/6)*y = 9
To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution:
From the first equation, we can express x in terms of y:
x = (18/2)*(2 - (5/6)*y)
Substituting this expression for x into the second equation, we get:
(7/9)*((18/2)*(2 - (5/6)*y)) + (1/6)*y = 9
Simplifying this equation will give us the value of y. Once we have y, we can substitute it back into the expression for x to find its value.
After solving the above equation, we get y = 24/5.
So, the quantity to be taken from cask A is:
x = (18/2)*(2 - (5/6)*(24/5)) = 24/5
Therefore, the ratio of the quantities to be taken from cask A and cask B is 24/5 : 24/5 = 1 : 1.
Hence, the correct answer is option B) 1:1.
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Two casks A and B are filled with two kinds of liquids. First and Second kind of liquids mixed in cask A in the ratio 2:7 and in cask B in the ratio 1:5 respectively. What quantity must be taken from each cask to form a mixture which shall consist of 2 litres of First Liquid and 9 litres of Second Liquid?a)4:7b)3:8c)5:6d)1:10e)2:1Correct answer is option 'B'. Can you explain this answer?
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