A man invested Rs.X at 15% p.a. at SI for 4 years and Rs. (1.35X) at 18% p.a. at SI for 3 years. If total interest received by man is Rs.15948, then find value of Rs. (3.12X).

Options

A. Rs.50544
B. Rs.42764
C. Rs.32580
D. Rs.37440

Answer

To solve the problem step by step, we will use the formula for Simple Interest (SI) and set up equations based on the information given in the question.

### Step 1: Understand the Problem
We have two investments:
1. Rs. X at 15% p.a. for 4 years.
2. Rs. 1.35X at 18% p.a. for 3 years.

The total interest received from both investments is Rs. 15,948.

### Step 2: Write the Formula for Simple Interest
The formula for Simple Interest is:
\[ \text{SI} = \frac{\text{Principal} \times \text{Rate} \times \text{Time}}{100} \]

### Step 3: Calculate the Interest from the First Investment
For the first investment of Rs. X at 15% for 4 years:
\[ \text{SI}_1 = \frac{X \times 15 \times 4}{100} = \frac{60X}{100} = 0.6X \]

### Step 4: Calculate the Interest from the Second Investment
For the second investment of Rs. 1.35X at 18% for 3 years:
\[ \text{SI}_2 = \frac{1.35X \times 18 \times 3}{100} = \frac{72.9X}{100} = 0.729X \]

### Step 5: Set Up the Equation for Total Interest
The total interest from both investments is given as Rs. 15,948. Therefore, we can write:
\[ \text{SI}_1 + \text{SI}_2 = 15,948 \]
Substituting the values we found:
\[ 0.6X + 0.729X = 15,948 \]

### Step 6: Combine Like Terms
Combine the terms on the left side:
\[ (0.6 + 0.729)X = 15,948 \]
\[ 1.329X = 15,948 \]

### Step 7: Solve for X
To find the value of X, divide both sides by 1.329:
\[ X = \frac{15,948}{1.329} \approx 12,000 \]

### Step 8: Calculate the Value of 3.12X
Now, we need to find the value of Rs. 3.12X:
\[ 3.12X = 3.12 \times 12,000 = 37,440 \]

### Step 9: Conclusion
The value of Rs. (3.12X) is Rs. 37,440.