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%?

• A. 50 gms
• B. 60 gms
• C. 30 gms
• D. 40 gms

Hint:

The silver amount never changes, only its percentage share drops as gold is added.

Answer 1

The Correct Option is A

There's a neater way to solve this, by tracking the silver instead of the gold, since silver never changes.

Silver in the original 50 gms of alloy is $20\%$ of 50, which is 10 gms. Adding pure gold does not change this 10 gms of silver at all.

After adding $x$ gms of gold, gold is 90% of the new mixture, so silver must be the remaining $10\%$ of the new mixture.

That gives the equation $10 = \frac{10}{100} \times (50 + x)$, so $50 + x = 100$, which means $x = 50$.

Let's summarize:

• Silver stays fixed at 10 gms throughout
• Silver share drops from 20% to 10%, so the new total must double to 100 gms
• Gold added: $x = 100 - 50 = 50$ gms

This confirms option A, 50 gms, without ever writing an equation in terms of gold.