Question

A person borrowed a sum of money with simple interest as given below:

(i) 6% per annum for the first three years

(ii) 8% per annum for the next five years

(iii) 12% per annum for the next four years

If he paid a total interest of Rs. 4,240, the money he borrowed (in rupees) is

1. 3,000
2. 3,500
3. 4,000
4. 4,050

Answer 1

Correct Answer - Option 3 : 4,000

Given:

Total Interest paid = Rs. 4,240

Rate of interest for first 3 years = 6%

Rate of interest for next 5 years = 8% 

Rate of interest for next 4 years = 12%

Formula used:

Simple interest = (Principal × Rate × Time)/100

Where, Simple interest = SI, Rate = R, Time = T

Calculation:

As we know that

Simple interest = (Principal × Rate × Time)/100

According to the question

SI₁ + SI₂ + SI₃ = [(P × R₁ × T₁)/100] + [(P × R₂ × T₂)/100] + [(P × R₃ × T₃)/100]

⇒ Rs. 4,240 = [(P × 6 × 3)/100] + [(P × 8 × 5)/100] + [(P × 12 × 4)/100]

⇒ 4240 = (18P/100) + (40P/100) + (48P/100)

⇒ 4240 = 106P/100

⇒ (4240 × 100)/106 = P

⇒ 40 × 100 = P

⇒ Rs. 4,000 = P

∴ The sum of money he borrowed is Rs. 4,000.