SSC CGL 2024 PYQ — Question 52

The correct answer is option 3 i.e. 70%.

Let the percentage increase the first time be x% and the second time be 2x%.

Initial price of the item = ₹1,000

Final price of the item = ₹2,295

So, $1000\times \left(1+\frac{x}{100} \right) \times \left(1+\frac{2x}{100} \right)=2295$

⇒ $\left(1+\frac{x}{100} \right) \times \left(1+\frac{2x}{100} \right)=2295/1000=2.295$

⇒ 1 + (3x/100) + (2x²/10000) = 2.295

⇒ (3x/100) + (2x²/10000) = 2.295 - 1 = 1.295

⇒ 300x + 2x² = 12950

⇒ 2x² + 300x - 12950 = 0

⇒ x² + 150x - 6475 = 0

⇒ x² + 185x - 35x - 6475 = 0

⇒ x(x + 185) - 35(x + 185) = 0

⇒ (x + 185)(x - 35) = 0

⇒ x = - 185 (Negative value not possible)

⇒ x = 35

⇒ 2x = 2 × 35 = 70

Therefore, the price increased the second time by 70%.