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The problem is written in Hindi and translates as follows:

**Problem:**
There is a mixture of gold and silver weighing 50 grams, in which 80% of the weight is gold. How much more gold should be added to the mixture so that the proportion of gold increases to 95%?

**Solution:**

Let the initial weight of gold in the mixture be:
\[
\text{Gold weight} = 80\% \text{ of } 50 \text{ grams} = \frac{80}{100} \times 50 = 40 \text{ grams}.
\]
The remaining 10 grams are silver.

Let the additional amount of gold to be added be \( x \) grams. After adding this gold, the total weight of the mixture will become:
\[
50 + x \text{ grams}.
\]

We want the proportion of gold in the new mixture to be 95%, so:
\[
\frac{40 + x}{50 + x} = 0.95.
\]

Now, solve this equation for \( x \):

1. Multiply both sides by \( 50 + x \):
\[
40 + x = 0.95 \times (50 + x).
\]

2. Expand the right-hand side:
\[
40 + x = 47.5 + 0.95x.
\]

3. Move all terms involving \( x \) to one side:
\[
40 + x - 0.95x = 47.5.
\]
\[
40 + 0.05x = 47.5.
\]

4. Subtract 40 from both sides:
\[
0.05x = 7.5.
\]

5. Solve for \( x \):
\[
x = \frac{7.5}{0.05} = 150 \text{ grams}.
\]

**Answer:**
150 grams of gold must be added to the mixture so that the proportion of gold becomes 95%.

Would you like any further details or have any questions?

Here are 5 related questions:
1. What if the initial proportion of gold was 70% instead of 80%?
2. How would the result change if the total mixture was 100 grams?
3. How can we check the final percentage of gold after adding the calculated amount?
4. What if we need to adjust the proportion to a different percentage, say 90%?
5. How would the problem change if instead of gold, the mixture contained copper and silver?

**Tip:** Always check the total weight and desired percentage carefully to avoid simple calculation errors.

50 ग्राम के मिश्रधातु में सोना और चांदी है। जिसमें सोने का भार 80% है। मिश्रधातु में कितना और सोना मिलाया जाए कि सोने का भाग 95% हो जाए?

Solve a real-world mixture problem where 50 grams of gold and silver contains 80% gold. Learn how much more gold to add to increase the gold percentage to 95%, using algebraic techniques and percentage concepts. Suitable for Grades 8-10.

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