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Question

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.

What is the ratio of the interest on the first loan to the interest on the second loan ?

This question was previously asked in
CDS 2 2026 Maths Question Paper (13-Sep-2026)
The correct answer is

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:

  1. **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.
  2. **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).
  3. **Total Interest:**
  4. **Ratio of Interests:**
    • \(SI_1 = 160 \times 10 = 1600\)
    • \(SI_2 = 320 \times 10 = 3200\)

Thus, the correct answer is 1:2.

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Similar Questions

  1. 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 \(n\)?
  2. What is the initial rate of interest per annum ?

Important Questions from Simple Interest

  1. 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 ?

  2. 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.

  3. 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?

  4. P borrowed an amount from Q at a simple interest of 10% p.a. At the end of the year, P paid back Rs 99000 which was 90% of what she owed. How much money did P borrow?

  5. An amount becomes Rs. 3795 in 3 years and Rs. 4537.50 in \(7 \frac{1}{2}\)  years on simple interest. Find the rate of interest per annum.

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