An investor earns 3% return on 1/4 of his capital, 5% on 2/3 and 11% on the remainder. What is the average rate of return he earns on his total capital?

Let
The investor total capital is x

Total return = 3% of (x/4) + 5% of (2x/3) + 11% of {x - (x/4) - (2x/3)}
= (3x/400) + (10x/300) + (11/100) of {(12x - 3x - 8x)/12}
= (3x/400) + (10x/300) + (11x/1200)
= (9x + 40x + 11x)/1200
= 60x/1200
= x/20

the average rate of return =[{(x/20)/x} × 100]%
= 5%