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

The correct answer is 900.

Let's define the variables for Kamala's investments. Let the amount invested in stocks be $S$, in bonds be $B$, and in gold be $G$.

We are given that the total investment is Rs 100,000. Therefore, we can write the first equation as:

$S+B+G=100000$

We are also given that the investment in bonds is 25% of the investment in gold. This can be expressed as:

$B=0.25G$

From this, we can multiply both sides by 4 to express $G$ in terms of $B$:

$G=4B$

Now, let's look at the returns. Kamala gained 10% on stocks, 6% on bonds, and 8% on gold, for a total gain of Rs 8200. This gives us our return equation:

$0.10S+0.06B+0.08G=8200$

Now we have a system of equations. Let's substitute $G=4B$ into our first total investment equation to express $S$ in terms of $B$:

$S+B+4B=100000$

$S+5B=100000$

$S=100000-5B$

Next, we substitute both $S=100000-5B$ and $G=4B$ into the total gain equation:

$0.10(100000-5B)+0.06B+0.08\left(4B\right)=8200$

Let's expand the terms and solve for $B$:

$10000-0.50B+0.06B+0.32B=8200$

Combine the $B$ terms ($-0.50+0.06+0.32=-0.12$):

$10000-0.12B=8200$

$10000-8200=0.12B$

$1800=0.12B$

$B=\frac{1800}{0.12}=15000$

So, Kamala invested Rs 15,000 in bonds. The question asks for the amount she gained specifically from the bonds, which is 6% of her bond investment:

$\text{Gain from bonds}=0.06\times 15000=900$

Therefore, she gained Rs 900 from the bonds.