Question : In 3 years, Rs. 3000 amounts to Rs. 3993 at $x$% compound interest compounded annually. The value of $x$ is ___.
Option 1: $10$
Option 2: $8$
Option 3: $5$
Option 4: $3\frac{1}{3}$
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Correct Answer: $10$
Solution : Principal = Rs. 3000, Amount = Rs. 3993, Time = 3 years and Rate of interest = $x$% Now, applying the formula of compound interest, Amount = $p(1+\frac{r}{100})^t$ ⇒ $3000(1+\frac{x}{100})^3=3993$ ⇒ $(1+\frac{x}{100})^3=\frac{3993}{3000}$ ⇒ $(1+\frac{x}{100})^3=\frac{1331}{1000}$ ⇒ $(1+\frac{x}{100})^3=(\frac{11}{10})^3$ ⇒ $1+\frac{x}{100}=\frac{11}{10}$ ⇒ $\frac{x}{100}=\frac{11}{10}–1$ ⇒ $x=\frac{1}{10}×100$ ⇒ $x=10$ Hence, the correct answer is $10$.
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