Rahul invested in a bank at a rate of $R\%$ compound annually for $t$ years. Find the value of $t$.

Statement (I): Raj invested Rs. 10,000 in scheme A at a rate of $R\%$ simple interest for 3 years and received Rs. 3000 as interest.

Statement (II): If Rahul invested a certain amount at compound interest for $t$ years at the rate of $X\%$, then he gets Rs. 1900 less interest than the interest he would get if he invested the same amount at simple interest at the same rate for 4 years.

Which of the statements is/are sufficient to find $t$?

Question

Rahul invested in a bank at a rate of $R\%$ compound annually for $t$ years. Find the value of $t$.

Statement (I): Raj invested Rs. 10,000 in scheme A at a rate of $R\%$ simple interest for 3 years and received Rs. 3000 as interest.

Statement (II): If Rahul invested a certain amount at compound interest for $t$ years at the rate of $X\%$, then he gets Rs. 1900 less interest than the interest he would get if he invested the same amount at simple interest at the same rate for 4 years.

Which of the statements is/are sufficient to find $t$?

Accepted Answer

**Solution:**

1. From Statement (I):
   - Raj invested Rs. 10,000 at simple interest rate $R\%$ for 3 years and earned Rs. 3000 interest.
   - Using simple interest formula: $SI = \frac{P 	imes R 	imes T}{100}$
   - Substitute values: $3000 = \frac{10000 	imes R 	imes 3}{100}$
   - Simplify: $3000 = 300 R \Rightarrow R = 10\%$

However, this only gives the rate $R$, not the time $t$ for Rahul's compound interest investment.

2. From Statement (II):
   - Rahul invested an amount at compound interest for $t$ years at rate $X\%$.
   - The interest from compound interest is Rs. 1900 less than the simple interest for 4 years at the same rate $X\%$.
   - Without knowing the principal or the exact rate $X$, we cannot find $t$.

3. Combining both statements:
   - Statement (I) gives $R = 10\%$ but no information about $X$ or principal.
   - Statement (II) involves $X$ and principal but no direct link to $R$ or $t$.

Therefore, neither statement alone nor together provides sufficient information to determine $t$.

**Answer:** (a) Neither statement (I) nor statement (II) alone is sufficient to answer the question.

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