Answer :
The investment in Fund B is $2000.
To understand the given question we first have to understand the logic of percentage and how it affect the return on Investment.
If an investment fund returns a profit on an investment then the profit is calculated by multiplying the investment with the profit(in decimal form).
For Example: If the investment is A and profit is x % then the profit is calculated by:
Profit =A×([tex]\frac{x}{100}[/tex])
Now in the given problem, let us consider the amount of investment into the Fund B be x.
Profit in Fund B=10%
Profit in Fund A is 3%.
Investment in Fund A=$5000
Total profit from both investments=3% of 5000+10% of x
[tex]=\frac{3}{100}\times 5000 + \frac{10}{100}\times x\\ =150+0.1x[/tex]
Now the total investment=5000+x
The combined profit for both the Investments is 150+0.1x
But the combined profit is 5% for both investments.
profit=[tex]5\% of(5000+x)[/tex]
[tex]=\frac{5}{100}\times (5000+x)\\=0.05\times5000+0.05x\\=250+0.05x[/tex]
Now the profit is same, so if we equate both the expressions of profit we get a linear equation in x.
[tex]\therefore 250+0.05x=150+0.1x\\or,250-150=0.1x-0.05x\\or,100=0.05x\\or,x=2000[/tex]
Thus we can conclude that she invested $2000 in the Fund B.
To learn more about Investment and Percentage :
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