One-third of a certain sum is invested at 3% per annum; one-sixth of the sum is invested at 6% per annum and remaining sum at 8% per annum. If the annual simple interest from all these investments is Rs. 600, the original sum is

Let original sum = Rs. $$6x$$

Sum invested at 3% = Rs. $$2x$$ and sum invested at 6% = Rs. $$x$$ and sum invested at 8% = Rs. $$3x$$

Simple interest = $$\frac{P\times r\times t}{100}$$

According to ques,

=> $$\frac{2x\times3\times1}{100}+\frac{x\times6\times1}{100}+\frac{3x\times8\times1}{100}=600$$

=> $$6x+6x+24x=60,000$$

=> $$x=\frac{60000}{36}=\frac{10,000}{6}$$

$$\therefore$$ Original sum = $$6\times\frac{10000}{6}=Rs.$$ $$10,000$$

=> Ans - (D)