Question

Kamala divided her investment of Rs 100000 between stocks, bonds, and gold. Her investment in bonds was 25% of her investment in gold. With annual returns of 10%, 6%, 8% on stocks, bonds, and gold, respectively, she gained a total amount of Rs 8200 in one year. The amount, in rupees, that she gained from the bonds, was:

Hint:

When a mixture investment problem involves fixed returns and proportional allocations, reduce variables using the percentage relationships first. This simplifies the system into a single solvable equation.

Answer 1

Correct Answer: 900

Approach: Three unknowns, but the gold-bond link \(B = 0.25G\) collapses everything to one variable. Express stocks and gold through \(B\), then read off the bond gain.

Step 1: Name the investments.
Let stocks \(= S\), bonds \(= B\), gold \(= G\) (in rupees).
\[ S + B + G = 100000. \]

Step 2: Use the bond-gold relation.
Bonds are \(25\%\) of gold: \(B = 0.25G\), so \(G = 4B\).
Substitute into the total:
\[ S + B + 4B = 100000 \Rightarrow S = 100000 - 5B. \]

Step 3: Write the gain equation.
Returns are \(10\%, 6\%, 8\%\):
\[ 0.10S + 0.06B + 0.08G = 8200. \]
Put \(S = 100000 - 5B\) and \(G = 4B\):
\[ 0.10(100000 - 5B) + 0.06B + 0.08(4B) = 8200. \]
\[ 10000 - 0.50B + 0.06B + 0.32B = 8200. \]
\[ 10000 - 0.12B = 8200. \]

Step 4: Solve for \(B\).
\[ 0.12B = 1800 \Rightarrow B = 15000. \]

Step 5: Gain from bonds.
\[ 0.06 \times 15000 = 900. \]

Gain from bonds = Rs 900.

Answer 2

Setting up the equations. Let the investment in gold be \(G\); bonds \(=0.25G\). Since stocks, bonds and gold add up to Rs 100000:
\[ S = 100000 - 0.25G - G = 100000-1.25G. \]
The total gain equation is
\[ 0.10S+0.06(0.25G)+0.08G=8200. \]
Substituting \(S\):
\[ 0.10(100000-1.25G)+0.015G+0.08G=8200 \Rightarrow 10000-0.125G+0.095G=8200 \Rightarrow 10000-0.03G=8200. \]
So \(0.03G=1800\Rightarrow G=60000\), giving bonds \(=0.25\times60000=15000\).
Gain from bonds \(=0.06\times15000=\) Rs 900.

Answer: Rs 900.