A sum of money when invested for 8 years on simple interest doubles itself. 1/3rd of the amount collected after 8 years is invested again on simple interest at double rate for 3 years. If the amount collected after 3 years is Rs. 21000 then find the sum invested initially.

Let principal be P and rate be r%. If P doubles in 8 years at simple interest, then P = (P × r × 8)/100, giving r = 12.5%. After 8 years, amount = 2P. One-third of this (2P/3) is reinvested at 2r = 25% for 3 years. Interest = (2P/3) × 25 × 3/100 = P/2. Total amount = 2P/3 + P/2 = (4P + 3P)/6 = 7P/6 = 21,000, giving P = 18,000.