A sum, when invested at 20% simple interest per annum, amounts to ₹2880 after 3 years. What is the simple interest (in ₹)on the same sum at the same rate in 2 year?

Correct option is A

Given: ​

Amount = ₹2880 

Rate(r) = 20% 

Time(t) = 3 year 

Formula Used: ​

Simple interest(S.I) = $$\frac{P \times r \times t}{100}$$ 

where P is principle

Amount = P + S.I 

Solution:  

Amount = P + S.I 

So, 

​$$2880 = P +\frac{P \times 20 \times 3}{100} \\ \ \\ 2880 = P\left(1 + \frac{3}{5}\right) \\ \ \\ 2880 = P \left(\frac{8}{5}\right) \\ \ \\ P = \frac{2880 \times 5}{8} = ₹1800$$

Now, Simple interest for 2 years on same rate ;

​$$=\frac{1800 \times 20 \times 2}{100} = ₹720$$ 

Alternate Method: ​

rate = 20 % = $$\frac{1}{5}$$ 

5 = Principle , 1 = SI for 1 year

So for 3 year SI = 3 

Amount  = 5 + 3 = 8 

8 unit = 28800 

1 unit = 360  

now for two year for same rate 20%  SI = 2 $$\times 360 = ₹720$$​