A man invested \(\frac{1}{3}\) of his capital at 8%, \(\frac{1}{4}\) at 10% and the remainder at 12%. If his annual income is ₹671, find the capital.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → ₹6600
The income from each part is simple interest for one year at that part’s rate; the three incomes add up to ₹671. The remainder is \(1-\frac{1}{3}-\frac{1}{4}=\frac{5}{12}\) of the capital.
Assuming the capital to be ₹1200:
\(\frac{1}{3}\) of it, ₹400 at 8%: ₹32
\(\frac{1}{4}\) of it, ₹300 at 10%: ₹30
\(\frac{5}{12}\) of it, ₹500 at 12%: ₹60
Total income from the three parts: \(32+30+60=\) ₹122
The real capital (the income is in proportion to the capital):
The real income is \(\displaystyle\frac{671}{122}=5.5\) times this income
So the real capital is \(1200\times5.5=\) ₹6600