Problem:
An alloy of gold and silver weighs 50 gm. It contains 80% gold. How many grams of gold should be added to the alloy so that the percentage of gold increases to 90? Correct answer is '50'. Can you explain this answer?

Solution:

Step 1: Understanding the problem
We have an alloy that contains both gold and silver. The total weight of the alloy is 50 grams. The alloy is composed of 80% gold, meaning that 80% of the weight of the alloy is gold. We need to find out how many grams of gold should be added to the alloy so that the percentage of gold increases to 90.

Step 2: Setting up the equation
Let's assume that x grams of gold need to be added to the alloy. After adding x grams of gold, the weight of the alloy will still be 50 grams, but the percentage of gold will increase to 90%.

Step 3: Calculating the weight of gold in the alloy
Currently, the alloy contains 80% gold. So, the weight of gold in the alloy is 80% of 50 grams, which is (80/100) * 50 = 40 grams.

Step 4: Calculating the weight of gold after adding x grams
After adding x grams of gold, the weight of gold in the alloy will be 40 + x grams.

Step 5: Calculating the percentage of gold after adding x grams
The weight of the alloy remains 50 grams, so the weight of silver in the alloy will be 50 - (40 + x) grams.

The percentage of gold after adding x grams can be calculated as:
((40 + x) / 50) * 100

Step 6: Setting up the equation
We need to find the value of x such that the percentage of gold after adding x grams is 90%. So, we can write the equation as:
((40 + x) / 50) * 100 = 90

Step 7: Solving the equation
Let's solve the equation to find the value of x:
((40 + x) / 50) * 100 = 90
40 + x = (90 * 50) / 100
40 + x = 45
x = 45 - 40
x = 5

Step 8: Checking the answer
To check if our answer is correct, we need to calculate the percentage of gold after adding 5 grams.
((40 + 5) / 50) * 100 = 45 * 2 = 90
The percentage of gold is indeed 90%.

Conclusion:
To increase the percentage of gold in the alloy from 80% to 90%, we need to add 5 grams of gold.