Mr. X invested one fourth of his capital at 8%, one third at 7% and the remaining part at 10%. If his annual simple interest on this investment is Rs 510, then the total capital invested by Mr. X is?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs. 6000
Simple interest for one year is \(\frac{P\times R}{100}\). The interest on the three parts is added and equated to Rs 510.
Capital \(=x\); the parts are \(\frac{x}{4}\) and \(\frac{x}{3}\), and the rest is \(\displaystyle x-\frac{x}{4}-\frac{x}{3}=\frac{5x}{12}\)
Interest on \(\frac{x}{4}\) at 8%: \(\displaystyle \frac{x}{4}\times\frac{8}{100}=\frac{2x}{100}\)
Interest on \(\frac{x}{3}\) at 7%: \(\displaystyle \frac{x}{3}\times\frac{7}{100}=\frac{7x}{300}\)
Interest on \(\frac{5x}{12}\) at 10%: \(\displaystyle \frac{5x}{12}\times\frac{10}{100}=\frac{50x}{1200}\)
Total interest, over a common denominator of 1200: \(\displaystyle \frac{24x+28x+50x}{1200}=\frac{102x}{1200}=510\)
Capital \(\displaystyle x=\frac{510\times1200}{102}=5\times1200=6000\)