Answer: (d) 8.97 %Solution: Let the total capital of the investor is Rs \(x\).Percentage return on parts of his capital.5% on his \(\frac{1}{4}\)th capital. $$ = 5 \ \% \ of \ \frac{x}{4} $$ $$ = \frac{5}{100} \times \frac{x}{4} $$ $$ = \frac{x}{80} $$ 10% on his \(\frac{2}{3}\)rd capital. $$ = 10 \ \% \ of \ \frac{2x}{3} $$ $$ = \frac{10}{100} \times \frac{2x}{3} $$ $$ = \frac{x}{15} $$ 12% on his remaining capital $$ = 12 \ \% \ of \ \left[x - \{\frac{x}{4} + \frac{2x}{3}\}\right] $$ $$ = 12 \ \% \ of \ \left[x - \frac{x}{4} - \frac{2x}{3}\right] $$ $$ = 12 \ \% \ of \ \left[\frac{12x - 3x - 8x}{12}\right] $$ $$ = 12 \ \% \ of \ \frac{x}{12} $$ $$ = \frac{12}{100} \times \frac{x}{12} $$ $$ = \frac{x}{100} $$ the total return.$$ = \frac{x}{80} + \frac{x}{15} + \frac{x}{100} $$ $$ = \frac{107x}{1200} $$ Hence the average rate of return. $$ = \frac{107x}{1200} \times \frac{100}{x} $$ $$ = 8.97 \ \% $$
Trick: Total percentage return from three parts of the capital = (5 + 10 + 12) % = 27 %Hence the average rate of return = \(\frac{27}{3}\) = \(9 \ \%\)Hence approximately average return is 9 %.