An Alloy of Gold,Silver and Bronze Contain 90% Bronze, 7% Gold and GMAT Problem Solving

Question: An alloy of gold,silverand bronze contain 90% bronze, 7% gold and3% silver.a second alloy of bronze and silver only is melted with the first and mixture contain 85% of bronze,5% of gold,10% of silver find the percentage of bronze in second alloy?

1. 75%
2. 72.5%
3. 70%
4. 67.5%
5. 65%

Answer: B

Solution and Explanation:

Approach Solution 1:

We can assume a value for the original alloy as we are working for %.

Taking 100 as our starting point, B:G:S is 90:7:3
Gold is now reduced to 5% by the addition of alloy A, but no further gold is introduced.

Consequently, 7% of the initial total is now 5% of the new total, and 5% of the new total equals 7.
Thus, the new total is 7*100/5 = 140
So, adding a new alloy, A, we get 140-100 = 40.

Let's now focus on the bronze.
Bronze accounts for 85% of the new total, or 140 * 85/100=119.
Therefore, the quantity of bronze in the new alloy, A, is increased by 119 - 90 = 29
So, the percentage of bronze in A is 100 * 29 / 40 = 72.5%

Hence, B is the correct answer.

Approach Solution 2:

Assume x grammes total for mixture 1, with B=0.9x G=0.07x S=0.03x.
Mixture 2: Totally assuming the y-gram, B=ay S=by (a is what we need to find)
Mixture 3: Total x + y gramme, B = 0.85 (x + y), S = 0.1 (x + y), and G = 0.05 (x + y).

See gold is not present in mixture 2, so gold in mixture 1 and 3 should be same
0.07x = 0.05(x+y)
x=5y/2 --> (1)

We must now determine how much bronze is present in combination 2:
Mixture 1 bronze + Mixture 2 bronze = Mixture 3 bronze
0.9x + ay = 0.85(x + y)
0.9x - 0.85x = 0.85y - ay
0.05x = (0.85 - a)y
sub eq (1)
(0.85 - a)y = 0.05 * 5y/2
a = 1.45/2 = 0.725

The correct answer is 72.5%.

Approach Solution 3:

Let the original alloy consisted of 100 units, thus it has 90 units of bronze, 7 units of gold, and 3 units of silver.
Let there be x units of bronze and y units of silver in the second alloy.

Therefore, the new alloy will contain a total of 100 + (x+y) units, which consists of (3+y) units of silver, (90+x) units of bronze, and 7 units of gold.
The new alloy has a composition of 85% bronze, 5% gold, and 10% silver. Thus, we have

We obtain (x+y) = 40 units by taking 5% of [100 + (x+y)] = 7.
Moreover, 85% of [100 + (x+y)] equals 90+x.
or (85/100)*140 = 90 + x, which, when solved, gives us x = 29 units.
Thus, the percentage of bronze in the second alloy is (29/40)*100, or 72.5%.
The correct answer is B.

“An alloy of gold,silver and bronze contain 90% bronze, 7% gold and" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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