Question

Alex’s father invested some amount of money in the bank on simple interest. The amount grew to ₹36,000 at the end of 2 years. He waited for another 5 years and got a final amount of ₹51,000. What was the principal amount that he invested at the beginning?

• A. ₹30,000
• B. ₹25,000
• C. ₹20,000
• D. ₹32,000

Answer 1

The correct option is A ₹30,000

Let's suppose Alex's father invested $x$ amount of money in the bank at interest rate $r$.

Given his amount grew to ₹36,000 in 2 years.
We know that, $Amount=Principal+\frac{Principal\times Rate\times Time}{100}$
$\Rightarrow 36000=x+\frac{x\times r\times 2}{100}\Rightarrow \frac{x\times r}{100}=\frac{36000-x}{2}\left[i\right]$

It is also given that after waiting for another 5 years he received ₹51,000.
$\Rightarrow 51000=x+\frac{x\times r\times 7}{100}\Rightarrow \frac{x\times r}{100}=\frac{51000-x}{7}\left[ii\right]$

Now, by $\left[i\right]$ and $\left[ii\right]$ we can say,
$\frac{51000-x}{7}=\frac{36000-x}{2}\Rightarrow 2\times (51000-x)=7\times (36000-x)\Rightarrow 102000-2x=252000-7x\Rightarrow 5x=150000\Rightarrow x=30000$

$\Rightarrow$ Alex's father invested ₹30,000 in the bank.
Hence, option a is correct.