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SSB Head Constable 2018 Official Paper (Conducted on 3 Jan 2021)

Option 4 : Rs. 1,750

Given:

Compound interest on a certain amount for two years is Rs. 291.2.

Simple interest on the same amount is Rs. 280.

The rate of interest is same in both the cases,

Concept Used:

Amount = Principal × \(\rm\left(1+\frac{r}{100}\right)^n\), where r is the rate of compound interest and n is the time.

Amount = Principal × \(\rm\left(1+\frac{rn}{100}\right)\), where r is the rate of simple interest and n is the time.

Calculation:

It can be observed that:

Amount on Compound Interest for 2 years - Amount on Simple Interest for 2 years = 291.2 - 280

⇒ P\(\rm\left(1+\frac{r}{100}\right)^2\) - P\(\rm\left(1+\frac{2r}{100}\right)\) = 11.2

⇒ P\(\rm \left(\frac{r}{100}\right)^2\) = 11.2

⇒ \(\rm \left(P\times\frac{r}{100}\right)\left(\frac{r}{100}\right)\) = 11.2 ... (1)

Also, \(\rm P\times\frac{r}{100}\times2=280\).

⇒ \(\rm P\times\frac{r}{100}=140\) ... (2)

Using equations (1) and (2), we get:

\(\rm \frac{r}{100}={11.2\over140}\)

⇒ r = 8.

Using equation (2), we get:

P = 14000 ÷ 8 = Rs. 1,750.