A sum, when invested at 10% simple interest per annum, amounts to Rs. 4560 after 2 years. What is the simple interest (in Rs.) on the same sum at the same rate of interest in 1 year?

Correct option is B

Given:

Amount after 2 years = Rs. 4560

Rate of interest = 10% p.a.

Time = 2 years

Formula Used:

Amount = Principal + Simple Interest

Simple Interest = $$\frac{P \times R \times T}{100}$$​​

Solution:

Let principal be P

Then,

4560 = P + $$\frac{P \times 10 \times 2}{100}$$​​

4560 = P + $$\frac{20P}{100}$$​​

4560 = $$P \left(1 + \frac{20}{100}\right)$$​​

4560 = $$P \times 1.2$$​​

P =$$\frac{4560}{1.2}$$​ = 3800

Simple Interest for 1 year = $$\frac{3800 \times 10 \times 1}{100} = 380$$​​

Thus, The simple interest in 1 year is Rs. 380

Alternate Solution: ​

​$$10\% = \frac{1 \rightarrow \text{SI}}{10\rightarrow \text{Principal}}$$  

SI for two year = 2 

Amount = 10 + 2 = 12 

12 unit = 4560 

1 unit = $$\frac{4560}{12} = 380$$ 

So, SI for 1 year = ₹ 380