Question

A commission agent allows a rebate of 10% to an investor while the company pays an interest of 9% on the investment. What rate of interest does the investor actually earn on his investment?

Answer 1

Hint: Here, the money invested by the investor is not mentioned so we will take it as Rs.100 and then we need to find the amount allowed when a rebate of 10 % is allowed and when the company pays an interest of 9% on investment.

Complete step-by-step answer:

Since we don't know what amount of money, investor invests. Let’s consider it as 100 Rs.
Now, the investor invests 10% of its which is nothing but 100-10 = 90 Rs.
Now according to the question, the company pays an interest of 9% on the investment.
So, the interest on Rs. 90 is Rs.9.
So, now we need to find the interest of Rs. 100. Let us consider it as x i.e..,
\[
  90 \to 9 \\
  100 \to x \\
 \]
On cross multiplication, we get
$x = \dfrac{{9 \times 100}}{{90}} = \dfrac{{900}}{{90}} = 10$.
So the interest on Rs.100 is Rs.10 i.e..,$10\% \left[ {\because \dfrac{{10 \times 100}}{{100}} = 10} \right]$
Hence, the rate of interest the investor actually earns on his investment is 10%.
Note: While solving these types of problems, we need to consider the amount as 100 when the amount is not mentioned and we need to know the basic conversions from the rupees to percentages such that the solution becomes easier to understand.