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There are two qualities of gold alloys 22 carat and 23 carat having different prices per gram, their volumes being 130 gm and 180 gm, respectively. After equal quantities were taken from both the alloys, the alloy removed from the 22-carat alloy was added to the 23-carat alloy and vice versa. The resulting two types of alloys now have the same price per gram. Find the quantity of alloy drawn out from each type. It is to be assumed that 100% gold is 24 carats.
  • a)
    58.66 gm
  • b)
    75.48 gm
  • c)
    81.23 gm
  • d)
    None of these
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
There are two qualities of gold alloys 22 carat and 23 carat having di...
To solve this problem, let's assume:
Let x grams be the quantity of alloy drawn out from the 22-carat alloy.
Let y grams be the quantity of alloy drawn out from the 23-carat alloy.

Let's calculate the quantity of gold in each alloy before and after the process.

1. Calculation before the process:
- The 22-carat alloy has a volume of 130 grams, which means it contains (22/24) * 130 = 110 grams of gold.
- The 23-carat alloy has a volume of 180 grams, which means it contains (23/24) * 180 = 172.5 grams of gold.

2. Calculation after the process:
- When x grams are drawn out from the 22-carat alloy, it will have (110 - x) grams of gold left.
- When y grams are drawn out from the 23-carat alloy, it will have (172.5 - y) grams of gold left.

Now, let's calculate the quantity of gold in the resulting alloys after the exchange.

3. Calculation after the exchange:
- The alloy removed from the 22-carat alloy (x grams) is added to the 23-carat alloy. So, the 23-carat alloy now has (172.5 - y + x) grams of gold.
- The alloy removed from the 23-carat alloy (y grams) is added to the 22-carat alloy. So, the 22-carat alloy now has (110 - x + y) grams of gold.

According to the problem, the resulting two types of alloys now have the same price per gram. This means that the price per gram of the resulting 22-carat alloy is the same as the price per gram of the resulting 23-carat alloy.

4. Calculation of the price per gram:
- The price per gram of the 22-carat alloy is given by (110 - x)/(130 - x) since the alloy now has (110 - x) grams of gold and a volume of (130 - x) grams.
- The price per gram of the 23-carat alloy is given by (172.5 - y + x)/(180 - y) since the alloy now has (172.5 - y + x) grams of gold and a volume of (180 - y) grams.

Since the price per gram is the same for both alloys, we can equate the two expressions:

(110 - x)/(130 - x) = (172.5 - y + x)/(180 - y)

Now, let's solve this equation to find the values of x and y.
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There are two qualities of gold alloys 22 carat and 23 carat having different prices per gram, their volumes being 130 gm and 180 gm, respectively. After equal quantities were taken from both the alloys, the alloy removed from the 22-carat alloy was added to the 23-carat alloy and vice versa. The resulting two types of alloys now have the same price per gram. Find the quantity of alloy drawn out from each type. It is to be assumed that 100% gold is 24 carats.a)58.66 gmb)75.48 gmc)81.23 gmd)None of theseCorrect answer is option 'B'. Can you explain this answer?
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