Armaan invested \(\frac{1}{8}\) of a certain sum at 5% per annum, \(\frac{3}{5}\) of the sum at 6% per annum and the remaining at 10% per annum, all at simple interest for two years. If the total interest received is Rs 1674, what is the total sum invested?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs 12000
The total interest is the sum of the interests on the three parts. Taking the whole sum as \(S\), each part is a fraction of \(S\).
Remaining part \(\displaystyle =1-\frac{1}{8}-\frac{3}{5}=\frac{40-5-24}{40}=\frac{11}{40}\) of \(S\)
Interest on \(\frac{1}{8}\) at 5% for 2 years \(\displaystyle =\frac{1}{8}\times\frac{10}{100}S=\frac{1}{80}S\)
Interest on \(\frac{3}{5}\) at 6% for 2 years \(\displaystyle =\frac{3}{5}\times\frac{12}{100}S=\frac{9}{125}S\)
Interest on \(\frac{11}{40}\) at 10% for 2 years \(\displaystyle =\frac{11}{40}\times\frac{20}{100}S=\frac{11}{200}S\)
Total interest \(\displaystyle =\left(\frac{1}{80}+\frac{9}{125}+\frac{11}{200}\right)S=\frac{25+144+110}{2000}S=\frac{279}{2000}S\)
\(\displaystyle \frac{279}{2000}S=1674\), so \(\displaystyle S=\frac{1674\times2000}{279}=6\times2000=12000\)
The total sum invested is Rs 12000.