An investor deposited a total amount of ₹24,000 into two separate simple interest accounts. The first account offers an annual interest rate of 18%, while the second account provides 12% per annum. If the total interest earned from both accounts combined at the end of 1 year amounts to ₹3,840, calculate the principal amount allocated to the first account.

The correct option is ₹16,000.

Let's solve the problem step-by-step using basic algebra and the formula for Simple Interest.

Step 1: Understand the given information

Total amount deposited = ₹24,000
Interest rate on the first account (R₁) = 18% per annum
Interest rate on the second account (R₂) = 12% per annum
Time period (T) = 1 year
Total interest earned from both accounts combined = ₹3,840

Step 2: Formulate equations

Let the principal amount deposited in the first account be $x$.

Then, the principal amount deposited in the second account will be $24000-x$.

The formula for Simple Interest (SI) is:

$\text{SI}=\frac{P\×R\×T}{100}$

Interest from the first account (SI₁):

${\text{SI}}_1=\frac{x\×18\×1}{100}=\frac{18x}{100}$

Interest from the second account (SI₂):

${\text{SI}}_2=\frac{(24000-x)\×12\×1}{100}=\frac{12\×(24000-x)}{100}$

Step 3: Set up and solve the total interest equation

Given that Total Interest = SI₁ + SI₂ = ₹3,840:

$\frac{18x}{100}+\frac{12\×(24000-x)}{100}=3840$

Multiply the entire equation by 100 to remove denominators:

$18x+12(24000-x)=384000$

Expand the terms:

$18x+288000-12x=384000$

Simplify like terms:

$6x+288000=384000$

Subtract 288,000 from both sides:

$6x=384000-288000$

$6x=96000$

Divide by 6:

$x=\frac{96000}{6}$

$x=16000$

Therefore, the principal amount allocated to the first account is ₹16,000.