SSC GD 2024 PYQ — Question 49

The correct answer is option 1 i.e. Rs. 3000.

A = $P \left(1 + \frac{r}{100}\right)^t$

( A) is the amount (Principal + Interest)

( P ) is the principal sum 

( r) is the rate of interest per annum = 15%

( t) is the time in years = 2 years

Compound Interest for 2 years = Rs. 967.5

⇒ A = P + (Compound Interest) = P + 967.5

⇒ P + 967.5 = $P \left(1 + \frac{15}{100}\right)^2$

⇒ P + 967.5 = $P \left(1 + 0.15\right)^2 = P \times 1.15^2$

⇒ P + 967.5 = P × 1.3225

⇒ 967.5 = P × 1.3225 - P

⇒ 967.5 = P(1.3225 - 1)

⇒ 967.5 = P × 0.3225

⇒ P = 967.5 / 0.3225 = 3000

The sum (principal) is Rs. 3000.