An investor receives a total of Rs.5,700 per annum in interest from 3 stocks yielding 4%, 5% and 8% per annum respectively. The amount at 4% is Rs.20,000 more than the amount invested at 5%, and the interest from the 8% investment is 8 times the interest from the 5% investment. Amount of money invested in each stock is:
Thank u
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As for your question, let's break it down. Let's call the amount invested at 5% as x.
According to the information given, the amount invested at 4% is Rs.20,000 more than the amount invested at 5%. So, the amount invested at 4% is x + Rs.20,000.
The interest from the 8% investment is 8 times the interest from the 5% investment. Let's calculate the interest from the 5% investment first. The interest from the 5% investment is 0.05x.
Therefore, the interest from the 8% investment is 8 * 0.05x = 0.4x.
Now, we know that the investor receives a total of Rs.5,700 in interest from the three stocks. So we can set up an equation:
0.04(x + Rs.20,000) + 0.05x + 0.08x = Rs.5,700
Solving this equation will give us the amount invested in each stock.
Let's represent the amount invested in the stock yielding 4% as x.
According to the problem, the amount invested in the stock yielding 5% is Rs.20,000 less than the amount invested in the 4% stock, so it can be represented as (x-20000).
The interest from the 8% investment is 8 times the interest from the 5% investment, so we can say:
0.08x = 8 * 0.05 * (x - 20000)
Simplifying the equation, we have:
0.08x = 0.4x - 80000
First, let's isolate the x term:
0.08x - 0.4x = -80000
-0.32x = -80000
Dividing both sides by -0.32, we get:
x = -80000 / -0.32
x = 250,000
So the amount invested in the stock yielding 4% is Rs.250,000.
The amount invested in the stock yielding 5% is (250,000 - 20,000) = Rs.230,000.
The amount invested in the stock yielding 8% is 8 * 0.05 * (250,000 - 20,000) = Rs.9000.
Therefore, the amount of money invested in each stock is Rs.250,000 in the 4% stock, Rs.230,000 in the 5% stock, and Rs.9000 in the 8% stock.
To find the amount of money invested in each stock, we can set up a system of equations based on the given information.
Let's denote the amount invested in the 4% stock as A, the amount invested in the 5% stock as B, and the amount invested in the 8% stock as C.
We know that the total interest received is Rs. 5,700, so we can write the equation:
0.04A + 0.05B + 0.08C = 5700 (equation 1)
Next, we are given that the amount invested at 4% is Rs. 20,000 more than the amount invested at 5%. This can be written as:
A = B + 20000 (equation 2)
We are also told that the interest from the 8% investment is 8 times the interest from the 5% investment. This can be written as:
0.08C = 8 * (0.05B) (equation 3)
Now, we have a system of three equations (equations 1, 2, and 3) with three unknowns (A, B, and C). We can solve this system to find the values of A, B, and C.
Using equations 2 and 3, we can substitute A and C in terms of B:
B + 20000 = B
0.08(8 * 0.05B) = 8 * (0.05B)
Simplifying equation 3, we get:
0.40B = 8 * 0.05B
0.40B = 0.40B
Now, we can substitute the values of A and B back into equation 1 to solve for C:
0.04A + 0.05B + 0.08C = 5700
0.04(B + 20000) + 0.05B + 0.08C = 5700
0.04B + 800 + 0.05B + 0.08C = 5700
0.09B + 0.08C = 4900
By using the equation 0.09B + 0.08C = 4900, we can solve for C.
Once we have the value of C, we can substitute it back into equation 2 to find the value of B.
Finally, we substitute the values of B and C back into equation 2 to find the value of A.
By solving these equations, we can determine the amount of money invested in each stock.
Let the amounts invested at the three rates be x,y,z. Now just write down the facts as given:
.04x + .05y + .08z = 5700
x = y + 20000
.08z = 8 * .05y
Now just solve for x,y,z.