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A sum when invested at 12 12\frac{1}{2}21​​% simple interest per annum amounts to ₹8,250 after 2 years. What is the simple interest in 1 year?
Question

A sum when invested at 12 12\frac{1}{2}​% simple interest per annum amounts to ₹8,250 after 2 years. What is the simple interest in 1 year?

A.

₹ 910

B.

₹ 1,650

C.

₹ 825

D.

₹ 1,700

Correct option is C

Given:

Rate = 1212%=252%12\frac{1}{2}\% = \frac{25}{2}\%​ per annum

Amount after 2 years = ₹8250

Time = 2 years

Formula Used:

SI = P×R×T100\frac{P \times R \times T}{100}​​

A = P + SI

Solution:

Let principal = P

SI for 2 years = A − P = ₹8250 − P

Now,

SI = P×252×2100=25P100=P4\frac{P \times \frac{25}{2} \times 2}{100} = \frac{25P}{100} = \frac{P}{4}​​

So,

A = P +P4=5P4 \frac{P}{4} = \frac{5P}{4} ​​

Now, 

5P4=8250\frac{5P}{4} = 8250​​

P = 8250×45 \frac{8250 \times 4}{5}​ = ₹6600

Now, SI for 1 year:

SI = 6600×252×1100=6600×25200\frac{6600 \times \frac{25}{2} \times 1}{100} = \frac{6600 \times 25}{200} = ₹825 

Alternate Solution: 

12.5% = 1SI 1 year8Principle\frac{1\rightarrow SI \ 1\ year}{8 \rightarrow Principle}  

for 2 year SI = 2 unit

Amount = 2 + 8 = 10 unit 

10 unit = ₹8250 

So, 1 unit = 825010=825\frac{8250}{10} = ₹825 (SI for 1 year)​

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