Divide ₹3000 in two parts such that the simple interest on first part for 4 years at 8% p.a. is equal to the simple interest on the second part for 2 years at 9% per annum.
.08*4 x = .09*2 (3000-x)
To solve this problem, we need to understand the concept of simple interest and how it is calculated.
Simple Interest (SI) can be calculated using the formula: SI = (PrT) / 100
Where,
SI is the simple interest
P is the principal amount (the initial amount)
r is the rate of interest per annum
T is the time period in years
Now, let's solve the problem step by step:
Step 1: Let's assume the first part of the amount is x. So, the second part will be ₹3000 - x.
Step 2: According to the problem, the simple interest on the first part for 4 years at 8% per annum is equal to the simple interest on the second part for 2 years at 9% per annum.
Using the formula for simple interest, we can calculate the interest on the first part:
SI1 = (x * 4 * 8) / 100
Similarly, we can calculate the interest on the second part:
SI2 = ((3000 - x) * 2 * 9) / 100
Step 3: Since these two interests are equal, we can set up an equation:
SI1 = SI2
(x * 4 * 8) / 100 = ((3000 - x) * 2 * 9) / 100
Simplifying the equation:
32x = 54000 - 18x
Step 4: Combine like terms:
50x = 54000
Step 5: Solve for x:
x = 54000 / 50
x = 1080
So, the first part of the amount is ₹1080, and the second part is ₹3000 - ₹1080 = ₹1920.
Therefore, you can divide ₹3000 into two parts, ₹1080 and ₹1920, such that the simple interest on the first part for 4 years at 8% per annum is equal to the simple interest on the second part for 2 years at 9% per annum.