Question

Ramesh invests 1,200 at 5% simple interest. How much additional money must he invest at 8% simple interest so that his total annual income will be equal to 6% of his total investment during this year?

• A. 500
• B. 600
• C. 1200
• D. 1500

Answer 1

The Correct Option is B

To solve this problem, we need to determine how much additional money Ramesh must invest at 8% simple interest so that his total annual income from all investments equals 6% of his total investment for the year. 

1. Calculate the annual income Ramesh gets from the initial investment:
   • Ramesh invests ₹1200 at 5% simple interest.
   • Using the formula for simple interest: \(SI = \frac{{P \times R \times T}}{100}\), where \(P = 1200\), \(R = 5\), and \(T = 1\) year.
   • Interest from ₹1200 at 5%: \(SI = \frac{{1200 \times 5 \times 1}}{100} = 60\).
2. Let the additional money Ramesh must invest at 8% be ₹\(x\).
3. Calculate the interest from the additional investment:
   • Simple interest from ₹\(x\) at 8%: \(SI = \frac{{x \times 8 \times 1}}{100} = \frac{8x}{100}\).
4. Set the total interest from both investments equal to 6% of the total investment:
   • Total investment = ₹1200 + ₹\(x\).
   • Total interest from both investments: ₹60 + ₹\(\frac{8x}{100}\).
   • 6% of the total investment: \(\frac{(1200 + x) \times 6}{100}\).
   • Equating the two, we have: \(60 + \frac{8x}{100} = \frac{(1200 + x) \times 6}{100}\).
5. Solve the equation for \(x\):
   • Multiply through by 100 to clear fractions: \(6000 + 8x = (1200 + x) \times 6\).
   • Expand and simplify: \(6000 + 8x = 7200 + 6x\).
   • Rearrange the terms: \(8x - 6x = 7200 - 6000\).
   • \(2x = 1200\).
   • Divide both sides by 2: \(x = 600\).
6. Therefore, Ramesh must invest an additional ₹600 at 8% simple interest. The correct option is 600.