Question:
An alloy of gold and silver weighs 50 gms and contains 80% gold. How much gold should be added to the alloy so that the percentage of gold increases to 90%?
An alloy of gold and silver weighs 50 gms and contains 80% gold. How much gold should be added to the alloy so that the percentage of gold increases to 90%?
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The silver amount never changes, only its percentage share drops as gold is added.
Updated On: Jul 14, 2026
- 50 gms
- 60 gms
- 30 gms
- 40 gms
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The Correct Option is A
Solution and Explanation
Step 1: Find the gold and silver present at the start.
Gold in the alloy \(= 80\% \text{ of } 50 = \frac{80}{100} \times 50 = 40\) gms. Silver in the alloy \(= 50 - 40 = 10\) gms.
Step 2: Set up an equation after adding \(x\) gms of gold.
New total weight \(= 50 + x\) gms, and new gold weight \(= 40 + x\) gms. We need gold to be 90% of the new total, so \(40 + x = \frac{90}{100}(50+x)\).
Step 3: Solve for \(x\).
Multiply out: \(40 + x = 45 + 0.9x\). Bring like terms together: \(x - 0.9x = 45 - 40\), so \(0.1x = 5\), giving \(x = 50\).
Step 4: Check the wrong options.
Option D, 40 gms, would only make gold roughly 89% of the new mix, not quite 90%, so it falls short. Option C, 30 gms, and option B, 60 gms, also fail to satisfy the equation when substituted back in.
Final Answer:
Gold to be added \[ \boxed{x = 50 \text{ gms}} \]
Gold in the alloy \(= 80\% \text{ of } 50 = \frac{80}{100} \times 50 = 40\) gms. Silver in the alloy \(= 50 - 40 = 10\) gms.
Step 2: Set up an equation after adding \(x\) gms of gold.
New total weight \(= 50 + x\) gms, and new gold weight \(= 40 + x\) gms. We need gold to be 90% of the new total, so \(40 + x = \frac{90}{100}(50+x)\).
Step 3: Solve for \(x\).
Multiply out: \(40 + x = 45 + 0.9x\). Bring like terms together: \(x - 0.9x = 45 - 40\), so \(0.1x = 5\), giving \(x = 50\).
Step 4: Check the wrong options.
Option D, 40 gms, would only make gold roughly 89% of the new mix, not quite 90%, so it falls short. Option C, 30 gms, and option B, 60 gms, also fail to satisfy the equation when substituted back in.
Final Answer:
Gold to be added \[ \boxed{x = 50 \text{ gms}} \]
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