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.
1 : 2
To solve the given problem, we'll apply the basics of Simple Interest (SI). The formula for simple interest is:
\(SI = \frac{P \times R \times T}{100}\)
where \(P\) is the principal amount, \(R\) is the rate of interest per annum, and \(T\) is the time period in years.
Let's break down the problem step-by-step:
- **First Loan:**
- Principal = ₹16,000
- Time = 1 year (since it's borrowed at the beginning of the year)
- Let the interest rate be \(R\%\) per annum.
- **Second Loan:**
- Principal = ₹24,000
- Time = 8 months (since it's borrowed after 4 months of the year), which equates to \(\frac{8}{12} = \frac{2}{3}\) of a year.
- Rate of interest = \(2R\%\) (which is double the first loan's interest rate).
- **Total Interest:**
- **Ratio of Interests:**
- \(SI_1 = 160 \times 10 = 1600\)
- \(SI_2 = 320 \times 10 = 3200\)
Thus, the correct answer is 1:2.
Similar Questions
- What is the initial rate of interest per annum ?
- 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?
