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An alloy of manganese, tin and bronze contains 90% bronze, 7% manganese and 3% tin. A second alloy of bronze and tin is melted with the first and the mixture contains 85% of bronze, 5% of manganese and 10% of tin. What is the percentage of bronze in the second alloy?
- a)67.5%
- b)72.5%
- c)77.5%
- d)82.5%
Correct answer is 'B'. Can you explain this answer?
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Verified Answer
An alloy of manganese, tin and bronze contains 90% bronze, 7% manganes...
Say M and N are the total volumes of first and second alloys respectively.
Say C, Z and T represent Copper, Tin and Zinc percentages respectively in second alloy.
⇒ C + Z + T = 100 …… Eq.1
Amount of copper in the mixture = 0.90M + (C/100) x N = 0.85 x (M + N)
⇒ 0.05M = (0.85 – C/100) x N
⇒ C = 85 – 5 x (M/N) ….. Eq.2
Amount of Zinc in the mixture = 0.07M + (Z/100) x N = 0.05 x (M + N)
⇒ 0.02M = (0.05 – Z/100) x N
⇒ Z = 5 – 2 x (M/N) ….. Eq.3
Amount of copper in the mixture = 0.03M + (T/100) x N = 0.10 x (M + N)
⇒ –0.07M = (0.10 – T/100) x N
⇒ T = 10 + 7 x (M/N) …… Eq.4
Given Zinc percent in second alloy is Zero
⇒ Z = 0
Eq.3 ⇒ 0 = 5 – 2 x (M/N)
⇒ M/N = 5/2
Substitute M/N = 5/2 in Eq.4
⇒ T = 10 + 7 x (5/2) = 10 + 17.5 = 27.5%
∴ Tin in second alloy = 27.5%
Most Upvoted Answer
An alloy of manganese, tin and bronze contains 90% bronze, 7% manganes...
For mass x of the first alloy, Bronze= 9x/10, Manganese= 7x/100, Tin= 3x/100.
Let's say this x mass of first alloy is mixed with mass y of second alloy. Mass of mixture= x+y.
Since, the second alloy does not contain manganese, mass of manganese in mixture is same as earlier= 7x/100.
But the percentage of manganese in the mixture= 5%.
Hence, [(7x/100)/x+y]*100= 5. Upon solving this, we get 2x=5y. Hence, y= 2x/5.
Now, let's say, percentage of Bronze in the second alloy= b%. So, the Bronze in y mass of second alloy= by/100.
Total mass of bronze = 9x/10 + by/100
New percentage of bronze= 85. Hence, mass of bronze in (x+y) mass of mixture = 85(x+y)/100.
So, 9x/10 + by/100 = 85(x+y)/100. Putting y= 2x/5 from above, x will get cancelled throughout, and b= 72.5%
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Community Answer
An alloy of manganese, tin and bronze contains 90% bronze, 7% manganes...
Given information:
- First alloy contains 90% bronze, 7% manganese, and 3% tin.
- Second alloy contains bronze and tin, and when mixed with the first alloy, the resulting mixture contains 85% bronze, 5% manganese, and 10% tin.
To find: The percentage of bronze in the second alloy.
Solution:
Assume that we have x% bronze in the second alloy.
Step 1: Writing the equation for the first alloy.
In the first alloy, the percentage of bronze is 90%. Therefore, if we take 100 grams of the alloy, it will contain:
- 90 grams of bronze
- 7 grams of manganese
- 3 grams of tin
Step 2: Writing the equation for the second alloy.
Let's assume that we have x% bronze in the second alloy. Therefore, if we take 100 grams of the second alloy, it will contain:
- x grams of bronze
- (100 - x) grams of tin
Step 3: Writing the equation for the mixture.
When we mix the first and second alloys, we get a mixture that contains 85% bronze, 5% manganese, and 10% tin. Therefore, if we take 100 grams of the mixture, it will contain:
- 85 grams of bronze
- 5 grams of manganese
- 10 grams of tin
Step 4: Solving the equations.
When we mix the two alloys, the total weight of the mixture will be the sum of the weights of the two alloys. Therefore, we can write:
Weight of bronze in the mixture = Weight of bronze in the first alloy + Weight of bronze in the second alloy
Using the above equation, we can write:
85 = (90/100) * 100 + (x/100) * 100
85 = 90 + x
x = 85 - 90
x = -5
This means that our assumption that the second alloy contains some bronze is incorrect. Therefore, the percentage of bronze in the second alloy is 0%.
Final answer: 0%.
- First alloy contains 90% bronze, 7% manganese, and 3% tin.
- Second alloy contains bronze and tin, and when mixed with the first alloy, the resulting mixture contains 85% bronze, 5% manganese, and 10% tin.
To find: The percentage of bronze in the second alloy.
Solution:
Assume that we have x% bronze in the second alloy.
Step 1: Writing the equation for the first alloy.
In the first alloy, the percentage of bronze is 90%. Therefore, if we take 100 grams of the alloy, it will contain:
- 90 grams of bronze
- 7 grams of manganese
- 3 grams of tin
Step 2: Writing the equation for the second alloy.
Let's assume that we have x% bronze in the second alloy. Therefore, if we take 100 grams of the second alloy, it will contain:
- x grams of bronze
- (100 - x) grams of tin
Step 3: Writing the equation for the mixture.
When we mix the first and second alloys, we get a mixture that contains 85% bronze, 5% manganese, and 10% tin. Therefore, if we take 100 grams of the mixture, it will contain:
- 85 grams of bronze
- 5 grams of manganese
- 10 grams of tin
Step 4: Solving the equations.
When we mix the two alloys, the total weight of the mixture will be the sum of the weights of the two alloys. Therefore, we can write:
Weight of bronze in the mixture = Weight of bronze in the first alloy + Weight of bronze in the second alloy
Using the above equation, we can write:
85 = (90/100) * 100 + (x/100) * 100
85 = 90 + x
x = 85 - 90
x = -5
This means that our assumption that the second alloy contains some bronze is incorrect. Therefore, the percentage of bronze in the second alloy is 0%.
Final answer: 0%.
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An alloy of manganese, tin and bronze contains 90% bronze, 7% manganese and 3% tin. A second alloy of bronze and tin is melted with the first and the mixture contains 85% of bronze, 5% of manganese and 10% of tin. What is the percentage of bronze in the second alloy?a)67.5%b)72.5%c)77.5%d)82.5%Correct answer is 'B'. Can you explain this answer?
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An alloy of manganese, tin and bronze contains 90% bronze, 7% manganese and 3% tin. A second alloy of bronze and tin is melted with the first and the mixture contains 85% of bronze, 5% of manganese and 10% of tin. What is the percentage of bronze in the second alloy?a)67.5%b)72.5%c)77.5%d)82.5%Correct answer is 'B'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about An alloy of manganese, tin and bronze contains 90% bronze, 7% manganese and 3% tin. A second alloy of bronze and tin is melted with the first and the mixture contains 85% of bronze, 5% of manganese and 10% of tin. What is the percentage of bronze in the second alloy?a)67.5%b)72.5%c)77.5%d)82.5%Correct answer is 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An alloy of manganese, tin and bronze contains 90% bronze, 7% manganese and 3% tin. A second alloy of bronze and tin is melted with the first and the mixture contains 85% of bronze, 5% of manganese and 10% of tin. What is the percentage of bronze in the second alloy?a)67.5%b)72.5%c)77.5%d)82.5%Correct answer is 'B'. Can you explain this answer?.
An alloy of manganese, tin and bronze contains 90% bronze, 7% manganese and 3% tin. A second alloy of bronze and tin is melted with the first and the mixture contains 85% of bronze, 5% of manganese and 10% of tin. What is the percentage of bronze in the second alloy?a)67.5%b)72.5%c)77.5%d)82.5%Correct answer is 'B'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about An alloy of manganese, tin and bronze contains 90% bronze, 7% manganese and 3% tin. A second alloy of bronze and tin is melted with the first and the mixture contains 85% of bronze, 5% of manganese and 10% of tin. What is the percentage of bronze in the second alloy?a)67.5%b)72.5%c)77.5%d)82.5%Correct answer is 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An alloy of manganese, tin and bronze contains 90% bronze, 7% manganese and 3% tin. A second alloy of bronze and tin is melted with the first and the mixture contains 85% of bronze, 5% of manganese and 10% of tin. What is the percentage of bronze in the second alloy?a)67.5%b)72.5%c)77.5%d)82.5%Correct answer is 'B'. Can you explain this answer?.
Solutions for An alloy of manganese, tin and bronze contains 90% bronze, 7% manganese and 3% tin. A second alloy of bronze and tin is melted with the first and the mixture contains 85% of bronze, 5% of manganese and 10% of tin. What is the percentage of bronze in the second alloy?a)67.5%b)72.5%c)77.5%d)82.5%Correct answer is 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
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