Out of a certain sum, \(\frac{1 }{3}\)rd is invested at 3%,\(\frac{1 }{6}\)th at 6% and the rest at 8%. If the simple interest for 2 years from all these investments amounts to Rs.600, find the original sum.

Rs.5000 Rs.6000 Rs.5200 Rs.5500

Rs.5000

Total interest = \(\frac{P\;×\;3\;×\;2}{100\;×\;3}\) + \(\frac{P\;×\;6\;×\;2}{100\;×\;6}\) + \(\frac{P\;×\;8\;×\;2}{100\;×\;2}\) = 600 ⇒ 12P = 60000 ⇒ Sum = ₨.5000