Question

Rahul borrowed a sum of money at simple interest of 5% per annum for the first 3 years, 7% per annum for the next 5 years, and 9% per annum for the period beyond 8 years. If he pays a total of ₹6800 as interest only at the end of 10 years, how much money did he borrow?

• A. ₹8000
• B. ₹9000
• C. ₹10000
• D. ₹12000

Answer 1

Answer:

C. ₹10000

Let the principal be (P).

Simple interest is calculated in parts.

Step 1: Break the time periods

• First 3 years at 5%

• Next 5 years at 7%

• Last 2 years (10 − 8) at 9%

Step 2: Compute interest for each part

First 3 years:

$SI_1 = \frac{P \times 5 \times 3}{100} = \frac{15P}{100}$

Next 5 years:

$SI_2 = \frac{P \times 7 \times 5}{100} = \frac{35P}{100}$

Last 2 years:

$SI_3 = \frac{P \times 9 \times 2}{100} = \frac{18P}{100}$

Step 3: Total interest

$SI = \frac{15P + 35P + 18P}{100} = \frac{68P}{100}$

Given:
$\frac{68P}{100} = 6800$

Step 4: Solve for (P)

$P = \frac{6800 \times 100}{68} = 10000$

Final Answer:

Borrowed amount = ₹10,000