Investment Returns on Bonds and Gold

Let investment in Gold = $G$. Then investment in Bonds $B = 0.25G = G/4$. Let investment in Stocks = $S$. $S + B + G = 100000 \implies S + 1.25G = 100000 \implies S = 100000 - 1.25G$. Total gain = $0.10S + 0.06B + 0.08G = 8200$. Substitute $S$ and $B$: $0.10(100000 - 1.25G) + 0.06(0.25G) + 0.08G = 8200$ $10000 - 0.125G + 0.015G + 0.08G = 8200$ $10000 - 0.03G = 8200 \implies 0.03G = 1800 \implies G = 60000$. Hence, $B = 0.25 \times 60000 = 15000$. Gain from bonds = $6\% \text{ of } 15000 = 0.06 \times 15000 = 900$. Wait, let's re-verify: $0.125 - 0.015 - 0.08 = 0.03$. Yes! $G = 60000$, $B = 15000$, Gain = 900.