Question

An investor earns 3% return on 1/4th of his capital, 5% on 2/3 rd and 11% on the remainder, What is the average rate of return he earns on his total capital? a) 5% b) 10% c) 5.5% d) 10.5%​

Answer 1

$(3 \times \frac{1}{4} ) + (5 \times \frac{2}{3}) + (11 \times (1 - ( \frac{1}{4} + \frac{2}{3} )) \\ = \frac{3}{4} + \frac{10}{3} + \frac{11}{12} \\ = 5 \: percent$

Answer 2

Answer:

The average rate of return he earns on his total capital is 5% (approximately)

Step-by-step explanation:

Let, total capital of investor be x rupees.

First given,

he earns 3% return on 1/4th of his capital.

$\frac{1}{4}$ th of capital =

$\frac{1}{4} \times x \\ = \frac{x}{4}$

and 3% of $\frac{x}{4}$

$= \frac{3}{100} \times \frac{x}{4} \\ = \frac{3x}{400} rupees$

Again given,

he earns 5% on 2/3 rd of capital.

$\frac{2}{3 } \: rd$ capital

$= \frac{2}{3} \: rd \: of \: x \\ = \frac{2}{3} \times x \\ = \frac{2x}{3} \: rupees$

and

$5\% \: on \: \frac{2x}{3} = \frac{5}{100} \times \frac{2x}{3} \\ = \frac{x}{30} \: rupees$

It is also given he earn 11% on the remainder.

Remainder part of capital x =

$x - ( \frac{x}{4} + \frac{2x}{3} ) \\ = x - \frac{3x + 8x}{12} \\ = x - \frac{11x}{12} \\ = \frac{11x}{12}$

Now,

$11\% \: of \: \frac{11x}{12} \\ = \frac{11}{100} \times \frac{11x}{12} \\ = \frac{121x}{1200} \: rupees$

Now,his total earn

$= \frac{3x}{400} + \frac{x}{30} + \frac{121x}{1200} \\ = \frac{9x + 40x + 121x}{1200} \\ = \frac{170x}{1200} \: rupees$

Here x rupees mean 100 %

So, 1 rupee mean $\frac{100}{x} \%$

170x/1200 mean

$\frac{170x}{1200} \times \frac{100}{x} \\ = \frac{170}{12} \\ = 14.17\%$

So, average rate of return he earns on his total capital

$= \frac{14.17}{3} \% \\ = 4.72\% \: \\ = 5\%(approximately)$

This is a problem of percentage.

Know more about percentage.

https://brainly.in/question/10002322

https://brainly.in/question/33820520