CTET Paper II (Mathematics and Science) 14 Dec 2024 Shift 1 Solved Paper

Concept:First calculate the time period using simple interest. Then find the compound amount for the same time at a different rate, handling fractional years by using compound interest for full years and simple interest for the remaining fraction.Explanation:Principal (P) = ₹8000, Amount = ₹9500, Rate = 7.5% per annum simple interest. Use simple interest formula: $A = P \left(1 + \frac{r \times x}{100}\right)$.Substitute: $9500 = 8000 \left(1 + \frac{7.5 \times x}{100}\right)$. Simplify: $\frac{9500}{8000} = 1 + 0.075x \Rightarrow 1.1875 = 1 + 0.075x$. So $0.1875 = 0.075x$ giving $x = \frac{0.1875}{0.075} = 2.5$ years.Now find amount for same principal ₹8000 at 20% per annum compounded yearly for 2.5 years.Apply compound interest for full years: first 2 years: $A_2 = 8000 \times (1 + 0.20)^2 = 8000 \times 1.44 = ₹11520$. For remaining half year, use simple interest on ₹11520 at 20% p.a.: $A = 11520 \times \left(1 + 0.20 \times 0.5\right) = 11520 \times 1.10 = ₹12672$.Answer:₹12672 (Option C)