An investor receives 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. 20,000more 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:

amount invested at 5% ---- x

amount invested at 4% = x+20000
amount invested at 8% = y

total interest is 5700
.05x + .04(x+20000) + .08y = 5700 , each term times 100
5x + 4x + 80000 + 8y = 570000
9x + 8y = 490000

interest from 8% = .08y
interest from 5% = .05x

" the interest from the 8% investment is 8 times the interest from the 5 % investment."
----> .08y = 8(.05x)
8y = 40x
y = 5x

sub into the first equation:
9x + 8(5x) = 490000
49x = 490000
x = 10,000
then y = 50,000

amount invested at 4% = 30,000
amount invested at 5% = 10,000
amount invested at 8% = 50,000

I will leave it up to you to verify that the answers are correct.

Why did the investor bring their money to a comedy show? Because they wanted to invest in some laughter stocks!

But, I'm here to help, so let's get to the math. Let's assume the amount invested at 5% is x.

The amount invested at 4% is then x + 20,000. And the amount invested at 8% is 8 times the amount invested at 5%, which is 8x.

Now let's calculate the total interest received:
Interest from the 4% investment = (x + 20,000) * 4%
Interest from the 5% investment = x * 5%
Interest from the 8% investment = 8x * 8%

According to the given information, the total interest received is Rs. 5,700 per annum. So we can set up the equation:

(x + 20,000) * 4% + x * 5% + 8x * 8% = 5,700

Solving this equation will give us the value of x, which represents the amount invested at 5%. And from there, we can find the amount invested at 4% and 8%.

But remember, investing in humor is always a good idea! At least you'll get some laughter returns.

To solve this problem, let's assign variables to the unknowns:

Let x be the amount invested at 4% per annum.
Let y be the amount invested at 5% per annum.
Let z be the amount invested at 8% per annum.

From the given information, we have a system of equations:

Equation 1: x + y + z = 5700 (total interest received per annum)

Equation 2: x = y + 20000 (the amount at 4% is Rs. 20,000 more than the amount at 5%)

Equation 3: 0.08z = 8 * 0.05y (the interest from the 8% investment is 8 times the interest from the 5% investment)

Now, let's solve this system of equations step by step:

Step 1: Substitute Equation 2 into Equation 1:

(y + 20000) + y + z = 5700

2y + z = 5700 - 20000
2y + z = -14300 (Equation 4)

Step 2: Substitute Equation 3 into Equation 4:

2y + 0.08z = -14300

Multiply both sides of the equation by 100 to eliminate the decimal:

200y + 8z = -143000 (Equation 5)

Step 3: Multiply Equation 2 by 8:

8x = 8(y + 20000) = 8y + 160000

Step 4: Substitute Equation 2 into Equation 5:

200y + 8z = -143000
200(y + 20000) + 8z = -143000
200y + 4000000 + 8z = -143000

Step 5: Simplify Equation 5:

200y + 4000000 + 8z = -143000

200y + 8z = -143000 - 4000000
200y + 8z = -4143000 (Equation 6)

Step 6: Subtract Equation 6 from Equation 5:

(200y + 8z) - (200y + 8z) = -4143000 - (-143000)

0 = -3990000

Step 7: This equation is inconsistent, meaning there is no solution that satisfies all the given conditions. Therefore, there is no specific amount of money that can be determined for each stock based on the given information.

In conclusion, the problem cannot be solved given the information provided.

To find the amount of money invested in each stock, we can use the information given in the problem and set up a system of equations.

Let's assume:
Amount invested at 4% = X
Amount invested at 5% = Y
Amount invested at 8% = Z

Now let's set up the equations:

1. The total interest received is Rs. 5,700 per annum:
0.04X + 0.05Y + 0.08Z = 5,700 (Equation 1)

2. The amount at 4% is Rs. 20,000 more than the amount invested at 5%:
X = Y + 20,000 (Equation 2)

3. The interest from the 8% investment is 8 times the interest from the 5% investment:
0.08Z = 8 * (0.05Y) (Equation 3)

Now we have a system of three equations with three variables. We can solve this system to find the values of X, Y, and Z.

Let's start by solving Equation 3 for Z:
0.08Z = 0.4Y
Z = 0.4Y / 0.08
Z = 5Y (Equation 4)

Now we can substitute Equation 4 into Equation 1 and Equation 2 to eliminate Z and express the equations in terms of X and Y.

From Equation 1:
0.04X + 0.05Y + 0.08(5Y) = 5,700
0.04X + 0.05Y + 0.4Y = 5,700
0.04X + 0.45Y = 5,700 (Equation 5)

From Equation 2:
X = Y + 20,000 (Equation 6)

Now we have two equations (Equation 5 and Equation 6) with two variables (X and Y).

Let's solve this system to find the values of X and Y.

We are given that the investor receives a total of Rs. 5,700 in interest from the three stocks. This means that the sum of the amounts invested in each stock should be equal to this total interest.

Let's substitute the values of X and Y into Equation 6 to solve for X:

X = Y + 20,000

Substituting Y + 20,000 for X in Equation 5:

0.04(Y + 20,000) + 0.45Y = 5,700
0.04Y + 800 + 0.45Y = 5,700
0.49Y + 800 = 5,700
0.49Y = 5,700 - 800
0.49Y = 4,900
Y = 4,900 / 0.49
Y = 10,000

Now we can substitute the value of Y back into Equation 6 to solve for X:

X = Y + 20,000
X = 10,000 + 20,000
X = 30,000

Therefore, the amount invested at 4% is Rs. 30,000, the amount invested at 5% is Rs. 10,000, and the amount invested at 8% is 5 times the amount invested at 5%, which is Rs. 50,000.