Question

Person A borrows rupees 4000 from another person B for a duration of 4 year rupee He borrows a portion of it at 3% simple interest per annum, while the rest at 4% simple interest per annum. If B gets rupees 520 as total interest, then the amount A borrowed at 3% per annum in rupee is …………….

Hint:

When solving problems involving simple interest, break the total interest into parts based on the different rates and use the formula for simple interest to set up an equation.

Answer 1

Step 1: Define variables. Let \( x \) be the amount borrowed at 3% interest per annum, and \( 4000 - x \) be the amount borrowed at 4% interest per annum. 
Step 2: Use the formula for simple interest. The formula for simple interest is: \[ \text{SI} = \frac{P \times R \times T}{100} \] where:
- \( P \) is the principal amount,
- \( R \) is the rate of interest,
- \( T \) is the time in yea\rupee
The interest for the amount borrowed at 3% is: \[ \text{SI}_1 = \frac{x \times 3 \times 4}{100} = \frac{12x}{100} \] The interest for the amount borrowed at 4% is: \[ \text{SI}_2 = \frac{(4000 - x) \times 4 \times 4}{100} = \frac{16(4000 - x)}{100} = \frac{64000 - 16x}{100} \] 
Step 3: Set up the equation for total interest. The total interest is given as \rupee 520. Therefore, we have: \[ \frac{12x}{100} + \frac{64000 - 16x}{100} = 520 \] 
Step 4: Solve the equation. Multiply the entire equation by 100 to eliminate the denominators: \[ 12x + 64000 - 16x = 52000 \] Simplify: \[ -4x + 64000 = 52000 \] \[ -4x = -12000 \] \[ x = 3000 \] Thus, the amount borrowed at 3% interest per annum is: \[ \boxed{380} \]