An investor earns 3% return on (1/4)^th of his capital, 5% on (2/3)^rd and 11% on the reminder. What is the average rate of return he earns on his total capital?

Let, the capital be x taka

Earns on 3% rate = (x/4) × 3/100 = 3x/400
Earns on 5% interest = (2x/3) × 5/100 = x/30

Remainder = x - (x/4) - (2x/3)
                 = x{1 - (11/12)}
                  = x/12
 
Earns on 11% interest = (x/12) × (11/100)
                                 = 11x/1200

Total return = (3x/400) + (x/30) + (11x/1200)
                  = (9x + 40x + 11x)/1200
                   = 60x/1200
                    = x/20

The average rate of return he earns on his total capital = {(x/20)/x} × 100% = 5%