CAT General Knowledge — practice by topic

To find 25% of a number, we can follow these steps: 1. **Convert the percentage to a fraction:** $$25\% = \frac{25}{100}$$ 2. **Simplify the fraction:** $$\frac{25}{100} = \frac{1}{4}$$ 3. **Multiply the fraction by the number:** $$\frac{1}{4} \times 480$$ 4. **Perform the division:** $$480 \div 4 = 120$$ Therefore, 25% of 480 equals **120**.

To find the final price after successive discounts, we apply each discount sequentially to the remaining balance. **Step 1: Calculate the price after the first 10% discount.** $$\text{Discount 1} = 10\% \text{ of } ₹1000 = \frac{10}{100} \times 1000 = ₹100$$ $$\text{Price after first discount} = 1000 - 100 = ₹900$$ **Step 2: Calculate the price after the second 20% discount.** Note that the 20% discount is applied to the **new** price of ₹900, not the original ₹1000. $$\text{Discount 2} = 20\% \text{ of } ₹900 = \frac{20}{100} \times 900 = ₹180$$ $$\text{Final Price} = 900 - 180 = ₹720$$ **Alternative Method (Multiplier):** You can multiply the original price by the remaining percentage for each discount: $$\text{Final Price} = 1000 \times (1 - 0.10) \times (1 - 0.20)$$ $$\text{Final Price} = 1000 \times 0.9 \times 0.8 = ₹720$$

To find the ratio $a:c$, we can express the given ratios as fractions and multiply them. 1. **Express ratios as fractions:** Given $a:b = 3:5$, we can write this as: $$\frac{a}{b} = \frac{3}{5}$$ Given $b:c = 4:7$, we can write this as: $$\frac{b}{c} = \frac{4}{7}$$ 2. **Multiply the fractions:** To isolate $a$ and $c$, we multiply $\frac{a}{b}$ by $\frac{b}{c}$ because the '$b$' terms will cancel out: $$\frac{a}{c} = \frac{a}{b} \times \frac{b}{c}$$ 3. **Substitute the values:** $$\frac{a}{c} = \frac{3}{5} \times \frac{4}{7}$$ $$\frac{a}{c} = \frac{3 \times 4}{5 \times 7} = \frac{12}{35}$$ 4. **Final Ratio:** The ratio $a:c$ is $12:35$.