Multiple choice

Natesh borrowed some money at rate $6\%$ p.a. for the first $3$ years, $9\%$ p.a. for the next five years and $13$ p.a. beyond $8$ years. The above are all simple interest rates. If Natesh pays a total of Rs. $8160$ as an interest after $11$ years , how much money did he borrow?

  1. Rs. $8000$
  2. Rs. $10000$
  3. Rs. $12000$
  4. Rs. $14000$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The total simple-interest rate over 11 years is 3 × 6% + 5 × 9% + 3 × 13% = 102%. Therefore, 1.02P = 8160, giving P = Rs. 8000.

AI explanation

Using the formula for simple interest with varying rates, SI = (P * R1 * T1)/100 + (P * R2 * T2)/100 + (P * R3 * T3)/100, the total interest of Rs. 8160 over 11 years is calculated by splitting the time periods. Substituting the rates and times gives 8160 = (P * 6 * 3)/100 + (P * 9 * 5)/100 + (P * 13 * 3)/100. Simplifying this results in 8160 = 18P/100 + 45P/100 + 39P/100, which further reduces to 8160 = 1.02P. Dividing 8160 by 1.02 gives the borrowed principal of Rs. 8000.

Keep practicing — related questions