The simple interest on a sum for 11 years is Rs. 42000. The rate of interest…
2024
The simple interest on a sum for 11 years is Rs. 42000. The rate of interest for the first 4 years is 3 percent per annum and for the next 7 years is 9 percent per annum. What is the sum?
- A.
Rs. 70000
- B.
Rs. 56000
- C.
Rs. 60000
- D.
Rs. 58000
Attempted by 35 students.
Show answer & explanation
Correct answer: B
To find the sum, we need to calculate the total simple interest based on the different rates applied over the specified time periods and equate it to the given total interest of Rs. 42,000.
Step-by-Step Calculation
Define the variables:
Let the Principal (the sum) be P.
Period 1: Time = 4 years, Rate = 3%
Period 2: Time = 7 years, Rate = 9%
Calculate interest for each period:
Simple Interest (SI) = (Principal × Rate × Time) / 100
SI for the first 4 years = (P × 3 × 4) / 100 = 12P / 100
SI for the next 7 years = (P × 9 × 7) / 100 = 63P / 100
Sum the interest and equate to the total:
Total Interest = 12P / 100 + 63P / 100 = 75P / 100
Given Total Interest = 42,000
75P / 100 = 42,000
Solve for P:
75P = 4,200,000
P = 4,200,000 / 75
P = 56,000