Question

A man took a loan of Rs 12000 with simple interest for as many years as the rate of interest per year.if he paid Rs 3000 as interest at the end of loan perio,what was the rate of interest​

Answer 1

Step-by-step explanation:

Solution,

Given,

Principal(P)= 12000

Interest(I)= 3000

Rate(R)= ?

Let rate = x% and time = x years

Then,

R= $(I*100) / (P*T)$       [Rate Formal]

x= (3000*1000) / (12000*x)

x^2 =300000/12000

x^2= 25

x=√25

x=5                  

Hence, the rate of interest was 5%.

Answer 2

Given: Loan amount = Rs. 12,000

           Loan period in years = Simple rate of interest per year

           Interest paid at the end of loan period = Rs. 3,000

To find: Rate of interest

Let: Rate of interest be $x$ % p.a. and time be $x$ years

Solution: Given that,

Principal = Rs. 12,000

Simple Interest = Rs. 3,000

Time = $x$ years

Interest rate = $x$ % p.a.

∵ $Simple \ Interest = \frac{Principal \ * \ Rate \ * \ Time}{100}$

⇒ $3,000 = \frac{12,000 \ * \ x \ * \ x}{100}$

⇒ $x^{2} = \frac{3,000 \ * \ 100}{12,000} = \frac{3,00,000}{12,000}$

⇒ $x^{2} = 25$

⇒ $x = \sqrt{25} =$ ± $5$

⇒ $x = 5$ (ignoring negative value as time or rate of interest can not be negative)

Hence, rate of interest was 5% p.a.