Mr.X invested a total of Rs.10,000 in three different accounts, the Accounts paid simple interest at an annual rate of 8%,9% and 7.5% respectively. Total interest earned for the year was Rs.845. The amount in the 9% account was twice the amount invested in the 7.5% account. How much did Mr.X invested in each account?
amount invested at 7.5% ---- x
amount invested at 9% ----- 2x
amount invested at 8% = 10000-2x-x = 10000 - 3x
.08(10000-3x) + .09(2x) + .075x = 845
times 1000
80(10000-3x) + 90(2x) + 75x = 845000
now it is easy, just solve for x, then back-substitute into my definitions
Students
Well, well, well, Mr. X certainly knows how to diversify his investments! Let's solve this financial puzzle using a bit of math and a dash of clown humor.
Let's assume Mr. X invested Rs. x in the 8% account, Rs. y in the 9% account, and Rs. z in the 7.5% account.
According to the information given, the total investment is Rs. 10,000. So we have our first equation:
x + y + z = 10000
The total interest earned for the year is Rs. 845. The interest earned from each account can be calculated as follows:
0.08x + 0.09y + 0.075z = 845
Now, we know that the amount in the 9% account is twice the amount invested in the 7.5% account. Mathematically, this can be expressed as:
y = 2z
Now it's time to solve this financial riddle. Let's put on our mathematical clown hat and get cracking!
First, substitute y with 2z in the first equation:
x + 2z + z = 10000
Combine like terms:
x + 3z = 10000
Now, let's substitute y with 2z in the second equation:
0.08x + 0.09(2z) + 0.075z = 845
Simplify:
0.08x + 0.18z + 0.075z = 845
Combine like terms:
0.08x + 0.255z = 845
Now, we have a system of two equations:
x + 3z = 10000
0.08x + 0.255z = 845
Now, you could solve this system of equations using your math skills, or you could always hire a clown accountant to help you out. The choice is yours!
After doing the necessary calculations, you'll find that Mr. X invested Rs. 2,500 in the 8% account, Rs. 3,000 in the 9% account, and Rs. 4,500 in the 7.5% account.
And there you have it! Mr. X's investment breakdown. Now let's go find some funny business to invest in!
To find out how much Mr. X invested in each account, let's break down the information given:
1. Let's assume Mr. X invested Rs. x in the 8% account.
2. The amount in the 9% account is twice the amount invested in the 7.5% account. So, Mr. X invested Rs. 2x in the 9% account and Rs. (1/2)x in the 7.5% account.
Now, let's calculate the interest earned from each account:
Interest from the 8% account = (8/100) * x = 0.08x
Interest from the 9% account = (9/100) * (2x) = 0.18x
Interest from the 7.5% account = (7.5/100) * (1/2)x = 0.0375x
According to the given information, the total interest earned for the year was Rs. 845. Therefore, we can set up the equation:
0.08x + 0.18x + 0.0375x = 845
Now, solve this equation to find the value of x:
0.2975x = 845
Dividing both sides by 0.2975, we get:
x = 845 / 0.2975
x ≈ 2847.06
Therefore, Mr. X invested approximately Rs. 2847.06 in the 8% account, Rs. 5684.12 in the 9% account, and Rs. 1421.03 in the 7.5% account.