Question

A worker borrowed some money on simple interest at the rate of 6% p. a. for the first 3 years, at the rate of 9% p. a. for the next 3 years, and at the rate of 14% p. a. for the period beyond 6 years. If he paid a total interest of Rs. 6,490 at the end of 7 years, how much money did he borrow?
1. Rs. 12,500
2. Rs. 11,000
3. Rs. 12,000
4. Rs. 10,000

Answer 1

Correct Answer - Option 2 : Rs. 11,000

Given:

A worker borrowed some money on simple interest at the rate of 6% p. a. for the first 3 years, at the rate of 9% p. a. for the next 3 years, and at the rate of 14% p. a. for the period beyond 6 years. If he paid a total interest of Rs.6,490 at the end of 7 years.

Concept used:

Simple interest 

Calculation:

Let the principal be x = 100

Si at the rate of 6% p. a. for 3 years 

⇒ 6 × 3 × x = 18x

Si at the rate of 9% p. a. for 3 years

⇒ 9 × 3 × x = 27x

Si at the rate of 14% p. a. for 1 year

⇒ 14 × x = 14x

As per the question,

⇒ 18x + 27x + 14x = 6490

⇒ 59x = 6490

⇒ x = 110

∴ Principal = Rs.11000