Abhishek invested an amount of Rs. 29.000 in two parts under two different schemes A and B and earned a total interest of Rs. 3,840. Schemes A and B offered `15%` and `12%` interest respectively. What was the amount invested in scheme 'A' ?

Options

A. Rs. 17,000
B. Rs.12,000
C. Rs.14,000
D. Data inadequate

Answer

To solve the problem, we need to determine how much Abhishek invested in scheme A. We know the total amount invested, the total interest earned, and the interest rates for both schemes.

Let's denote:
- The amount invested in scheme A as \( x \).
- The amount invested in scheme B as \( 29000 - x \) (since the total investment is Rs. 29,000).

The interest earned from scheme A can be calculated using the formula for simple interest:
\[ \text{Interest from A} = \frac{x \times 15 \times t}{100} \]
The interest earned from scheme B is:
\[ \text{Interest from B} = \frac{(29000 - x) \times 12 \times t}{100} \]
The total interest earned from both schemes is given as Rs. 3,840:
\[ \text{Interest from A} + \text{Interest from B} = 3840 \]

Substituting the expressions for the interest from A and B into the equation, we have:
\[ \frac{x \times 15 \times t}{100} + \frac{(29000 - x) \times 12 \times t}{100} = 3840 \]

We can factor out \( t \) and simplify:
\[ t \left( \frac{15x + 12(29000 - x)}{100} \right) = 3840 \]

Now, let's simplify the expression inside the parentheses:
\[ 15x + 12(29000 - x) = 15x + 348000 - 12x = 3x + 348000 \]

So the equation becomes:
\[ t \left( \frac{3x + 348000}{100} \right) = 3840 \]

Now, we can multiply both sides by 100 to eliminate the fraction:
\[ t(3x + 348000) = 384000 \]

Next, we can express \( t \) in terms of \( x \):
\[ t = \frac{384000}{3x + 348000} \]

Since \( t \) must be the same for both schemes, we can substitute this back into the interest equations to find \( x \). However, we can also solve for \( x \) directly by assuming \( t = 1 \) year for simplicity (as the problem does not specify the time period).

Thus, we can set:
\[ 3x + 348000 = 384000 \]
\[ 3x = 384000 - 348000 \]
\[ 3x = 36000 \]
\[ x = \frac{36000}{3} = 12000 \]

Therefore, the amount invested in scheme A is Rs. 12,000.

### Final Answer:
The amount invested in scheme A is Rs. 12,000.