The following questions are accompanied by two statements (I) and (II). You have to determine which statements(s) is/are sufficient/ necessary to answer the questions.
What is the C.I. on a sum at the end of 3 years?
I. C.I.at the end of two years is Rs. 110.
II. Difference between Cl and SI at the end of two year is Rs. 100 and rate percent is 10%.

Options

A. Only I
B. Only II
C. Either I or II
D. Only I and II

Answer

To determine the compound interest (C.I.) on a sum at the end of 3 years, we will analyze the two statements provided.

**Step 1: Analyze Statement I**
- Statement I states that the C.I. at the end of 2 years is Rs. 110.
- This information alone does not provide sufficient details about the principal amount or the rate of interest. Without knowing the principal, we cannot calculate the C.I. for 3 years.

**Conclusion for Statement I:** Not sufficient.

**Step 2: Analyze Statement II**
- Statement II provides two pieces of information:
1. The difference between C.I. and S.I. (Simple Interest) at the end of 2 years is Rs. 100.
2. The rate of interest is 10%.

- We can use the formula for the difference between C.I. and S.I. for 2 years:
\[ \text{Difference} = \frac{P \times r^2}{100^2} \]
where \( P \) is the principal and \( r \) is the rate of interest.

- Given that the difference is Rs. 100 and the rate is 10%, we can set up the equation:
\[ 100 = \frac{P \times (10)^2}{100^2} \]
Simplifying this:
\[ 100 = \frac{P \times 100}{10000} \]
\[ 100 = \frac{P}{100} \]
\[ P = 10000 \]

**Step 3: Calculate C.I. for 3 Years**
- Now that we have the principal \( P = 10000 \), we can calculate the amount at the end of 3 years using the formula:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
where \( n \) is the number of years.

- Plugging in the values:
\[ A = 10000 \left(1 + \frac{10}{100}\right)^3 = 10000 \left(1.1\right)^3 \]
\[ A = 10000 \times 1.331 = 13310 \]

- The C.I. is then calculated as:
\[ C.I. = A - P = 13310 - 10000 = 3310 \]

**Conclusion for Statement II:** Sufficient.

**Final Conclusion:**
- Statement I is not sufficient to answer the question.
- Statement II is sufficient to answer the question.

**Answer:** Only Statement II is sufficient.

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