Question

Alex invested his savings in two parts. The simple interest earned on the first part at 15% per annum for 4 years is the same as the simple interest earned on the second part at 12% per annum for 3 years. Then, the percentage of his savings invested in the first part is

• A. 62.50%
• B. 37.50%
• C. 60%
• D. 40%

Answer 1

The Correct Option is B

The correct answer is B: 37.50%
Alex divided his savings into two parts: one invested at a 15% annual interest rate for 4 years, and the other invested at a 12% annual interest rate for 3 years.
Let's denote the amount invested in the first part as ₹x and in the second part as ₹y.
The interest earned from the first part is calculated as \(0.15\times{x}\times4\), and the interest earned from the second part is calculated as \(0.12\times{y}\times3\).
Equating these two interests:
\(0.15\times{x}\times4=0.12\times{y}\times3\)
Solving for x and y:
20x=12y
This implies the ratio of x to y is 3:5.
Therefore, the percentage of savings invested in the first part is \(\frac{3}{(3+5)}=\frac{3}{8}=0.375\).
Converting this to a percentage gives us 37.5%.
So, Alex invested 37.5% of his savings in the first part.

Answer 2

Let the saving invested in first part be \(x\) and saving invested in second part be \(y\).
Given that,
\(\frac {x\times 15\times 4}{100}=\frac {y\times 12\times 3}{100}\)
\(x\times 15\times 4=y\times 12\times 3\)
\(60x=36y\)
\(\frac xy=\frac {36}{60}\)

\(\frac xy=\frac {3}{5}\)
Required percentage,
\(= \frac {x}{x+y}\times100\)

\(= \frac {3}{3+5}\times100\)

\(= \frac {3}{8}\times100\)
\(=37.50 \%\)

So, the correct option is (B): \(37.50\)