Question

At what rate, will a person who invests Rs. 2,000 will receive Rs.2, 090 as simple interest
in 9 months?
(a) 5%
(b)6%
(c) 10%
(d)None of these
​

Answer 1

Given :

Principle amount :- ₹2000

Simple Interest :- ₹2090

Time :- 9 months

To find :

The rate of interest applied to the person.

Solution :

As we know that, to calculate the rate of interest we are required with the time in years. But, in this question we are given in months. So, let's convert it to years.

${\sf \dashrightarrow 9 \: months = \dfrac{9}{12}}$

${\sf \dashrightarrow \cancel \dfrac{9}{12} = \dfrac{3}{4}}$

${\sf \dashrightarrow \dfrac{3}{4} = 0.75}$

Now, let's find the rate of interest.

Rate of interest :

${\sf \dashrightarrow \dfrac{SI \times 100}{P \times T}}$

${\sf \dashrightarrow \dfrac{2090 \times 100}{2000 \times 0.75}}$

${\sf \dashrightarrow \dfrac{2090 \times 1}{20 \times 0.75}}$

${\sf \dashrightarrow \dfrac{104.5 \times 1}{1 \times 0.75}}$

${\sf \dashrightarrow \dfrac{104.5}{0.75} = \dfrac{10450}{75}}$

${\sf \dashrightarrow \cancel \dfrac{10450}{75} = 139.33}$

Hence, the rate of interest is 139.33%.

Thus, Option D - None of these, is correct answer.