A person borrows a sum of ₹16,000 on simple interest at the beginning of a year. After 4 months, ₹24,000 more is borrowed at a rate of interest double the previous one. At the end of the year, the total interest on both the loans is ₹4800.
10%
To determine the initial rate of interest per annum, we need to analyze the situation described:
The total interest earned at the end of the year is ₹4800, considering two separate borrowings:
- The first borrowing is ₹16,000 for the entire year at a rate of interest \( r \% \).
- The second borrowing is ₹24,000 for the remaining 8 months of the year at a rate of interest double the initial one, i.e., \( 2r \% \).
The formula for simple interest is given by:
\(SI = \frac{P \times R \times T}{100}\)
For the first loan:
- Principal, \( P_1 = \) ₹16,000
- Rate of interest, \( R_1 = r \% \)
- Time, \( T_1 = 1 \) year
Simple interest for the first loan:
\(SI_1 = \frac{16000 \times r \times 1}{100} = 160r\)
For the second loan:
- Principal, \( P_2 = \) ₹24,000
- Rate of interest, \( R_2 = 2r \% \)
- Time, \( T_2 = \frac{8}{12} = \frac{2}{3} \) year
Simple interest for the second loan:
\(SI_2 = \frac{24000 \times 2r \times \frac{2}{3}}{100} = 320r\)
Total simple interest is given by:
\(SI_1 + SI_2 = 160r + 320r = 480r\)
We know the total interest is ₹4800, hence:
\(480r = 4800\)
Solving for \( r \):
\(r = \frac{4800}{480} = 10\%\)
Therefore, the initial rate of interest per annum is 10%. Thus, the correct answer is:
- Option:
10%
Similar Questions
- What is the ratio of the interest on the first loan to the interest on the second loan ?
- A sum of money invested at simple interest triples itself in 8 years and becomes \(n\) times in 20 years. What is the value of \(n\)?
Important Questions from Simple Interest
How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest ?
Nirav and Mehul borrowed Rs.4000 and Rs.5000 respectively for 2.5 years at the rate of x% per annum. Mehul paid Rs 125 more interest than Nirav. Find x.
If the interest on a sum of Rs.1200 is more than the interest on Rs.1000 by Rs.120 in three years, then what is the rate of interest per annum?.
The difference between the simple interest received from two banks on Rs. 500 for two years is Rs. 2.50. What is the difference between their rates?
A sum of Rs.1200 becomes Rs.1560 at a rate of simple interest in 3 years. In how many years will the sum of Rs.800 amount to Rs.1120 at the same rate of simple interest?
