A man has Rs. 10,000 to invest. He invests Rs. 4000 at 5% and Rs. 3500 at 4%. In order to have a yearly income of Rs. 500, he must invest the remaining Rs. 2500 at what rate of interest?

6.2%

6.3%

6.4%

Investment at 5%: Rs. 4000 x 5% = Rs. 200 per year

Investment at 4%: Rs. 3500 x 4% = Rs. 140 per year

Total income so far: Rs. 200 + Rs. 140 = Rs. 340 per year

Shortfall: Rs. 500 (desired income) - Rs. 340 (current income) = Rs. 160 per year

Amount to invest: Rs. 2500 (remaining amount)

Rate of interest required: (Rs. 160 / Rs. 2500) x 100% ≈ 6.4%

So, the correct answer is: 6.4%