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Two alloys contain gold and silver in the ratio of 3:7 and 7:3 respectively. In what ratio these alloys must be mixed with each other so that we get a alloy of gold and silver in the ratio of 2:3?
- a)2:1
- b)3:1
- c)4:3
- d)3:5
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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Two alloys contain gold and silver in the ratio of 3:7 and 7:3 respect...
Answer – B.3:1 Explanation : Gold = 3/10 and silver = 7/10 – in 1 vessel gold = 7/10 and silver = 3/10 – in 2 vessel let the alloy mix in K:1, then (3k/10 + 7/10)/ (7k/10 + 3/10) = 2/3. Solve this equation , u will get K = 3
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Two alloys contain gold and silver in the ratio of 3:7 and 7:3 respect...
Given:
- Two alloys with gold and silver in the ratio of 3:7 and 7:3 respectively
- Required alloy with gold and silver in the ratio of 2:3
To find:
- Ratio in which the two alloys must be mixed
Solution:
Let us assume that the first alloy has 3x amount of gold and 7x amount of silver, and the second alloy has 7y amount of gold and 3y amount of silver.
To obtain the required ratio of 2:3, we need to mix the two alloys in such a way that the resulting alloy has 2x amount of gold and 3x amount of silver.
Let us find the amount of gold and silver in the mixture:
- Gold in the mixture = 3x + 7y
- Silver in the mixture = 7x + 3y
We need to find the values of x and y such that the above equations are satisfied and the ratio of gold and silver in the mixture is 2:3.
From the given ratio of the first alloy, we have:
- (3x)/(7x) = 3/7
- x = 7/3
From the given ratio of the second alloy, we have:
- (7y)/(3y) = 7/3
- y = 3/7
Substituting the values of x and y in the equations for gold and silver in the mixture, we get:
- Gold in the mixture = 3(7/3) + 7(3/7) = 14
- Silver in the mixture = 7(7/3) + 3(3/7) = 28/3
Therefore, the ratio in which the two alloys must be mixed is:
- Gold to silver = 2:3
- Total amount of gold to total amount of silver = 14:(28/3) = 42:28 = 3:2
Hence, the correct answer is option B) 3:1.
- Two alloys with gold and silver in the ratio of 3:7 and 7:3 respectively
- Required alloy with gold and silver in the ratio of 2:3
To find:
- Ratio in which the two alloys must be mixed
Solution:
Let us assume that the first alloy has 3x amount of gold and 7x amount of silver, and the second alloy has 7y amount of gold and 3y amount of silver.
To obtain the required ratio of 2:3, we need to mix the two alloys in such a way that the resulting alloy has 2x amount of gold and 3x amount of silver.
Let us find the amount of gold and silver in the mixture:
- Gold in the mixture = 3x + 7y
- Silver in the mixture = 7x + 3y
We need to find the values of x and y such that the above equations are satisfied and the ratio of gold and silver in the mixture is 2:3.
From the given ratio of the first alloy, we have:
- (3x)/(7x) = 3/7
- x = 7/3
From the given ratio of the second alloy, we have:
- (7y)/(3y) = 7/3
- y = 3/7
Substituting the values of x and y in the equations for gold and silver in the mixture, we get:
- Gold in the mixture = 3(7/3) + 7(3/7) = 14
- Silver in the mixture = 7(7/3) + 3(3/7) = 28/3
Therefore, the ratio in which the two alloys must be mixed is:
- Gold to silver = 2:3
- Total amount of gold to total amount of silver = 14:(28/3) = 42:28 = 3:2
Hence, the correct answer is option B) 3:1.
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