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Consider the following question and deci...

Consider the following question and decide which of the statements is sufficient to answer the question. The simple interest on a sum of money is 100. What is the sun?
Statements:
I. The interest rate is 20% per annum.
II. The sum eamed simple interest in 5 years. Options are (a) Both statements I and II are sufficient (b) Only statement I is sufficient (c) Only statement II is sufficient (d) Either statement I or II is sufficient.

A

Both statements I and II are sufficient

B

Only statement I is sufficient

C

Only statement II is sufficient

D

Either statement I or II is sufficient

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to determine the principal amount (sum) based on the given simple interest (SI) of 100. We will analyze the two statements provided to see if they are sufficient to find the principal. ### Step-by-Step Solution: 1. **Understand the Simple Interest Formula**: The formula for simple interest is given by: \[ SI = \frac{P \times R \times T}{100} \] where: - \( SI \) = Simple Interest - \( P \) = Principal (the sum we want to find) - \( R \) = Rate of interest (in percentage) - \( T \) = Time (in years) 2. **Given Information**: - Simple Interest (SI) = 100 - We need to find the principal \( P \). 3. **Evaluate Statement I**: - Statement I states that the interest rate \( R \) is 20% per annum. - Plugging this into the formula along with the known SI: \[ 100 = \frac{P \times 20 \times T}{100} \] - We still have two variables: \( P \) and \( T \). Without knowing \( T \), we cannot find \( P \) uniquely. **Conclusion for Statement I**: Not sufficient alone. 4. **Evaluate Statement II**: - Statement II states that the sum earned simple interest in 5 years (i.e., \( T = 5 \)). - If we substitute \( T = 5 \) into the SI formula, we still need the rate \( R \) to find \( P \): \[ 100 = \frac{P \times R \times 5}{100} \] - Again, we have two variables: \( P \) and \( R \). Without knowing \( R \), we cannot find \( P \) uniquely. **Conclusion for Statement II**: Not sufficient alone. 5. **Combine Both Statements**: - From Statement I, we have \( R = 20\% \) and from Statement II, we have \( T = 5 \). - Now we can substitute both values into the SI formula: \[ 100 = \frac{P \times 20 \times 5}{100} \] - Rearranging gives: \[ 100 = \frac{P \times 100}{100} \] \[ 100 = P \] **Conclusion**: By using both statements together, we can find that the principal \( P = 100 \). ### Final Answer: Both statements I and II are necessary to answer the question. Therefore, the correct option is: **(a) Both statements I and II are sufficient.**
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