Question 1

Direction :"You are presented with two quantities, labeled as Quantity I and Quantity II. Your task is to solve both quantities and determine the correct relationship between Quantity I and Quantity II. After solving, choose the appropriate option t…

Accepted Answer

Concept & Quadratic Roots & Percentages: Quantity I involves solving a quadratic equation to find a percentage variable, which is then used to reverse-calculate the total income based on sequential spending. Quantity II tests basic algebraic manipulation and emphasizes the dual roots (positive and negative) of a quadratic function P^2 = k. Remaining Amount = Initial × (1 - (R/100)) Step-by-Step Solution: Solving Quantity I: 1. Solve the quadratic equation for y: 7y^2 - 476y + 8092 = 0 Divide the entire equation by 7: y^2 - 68y + 1156 = 0 This is a perfect square: (y - 34)^2 = 0 \implies y = 34. 2. Tarun spends 34% on education. Remaining income = (100 - 34)% = 66% of Total Income. 3. He spends 1/3 of the remaining on house rent: House rent = (1/3) × 66% = 22% of Total Income. 4. Given that the amount spent on house rent is ₹12826: 22% of Income = 12826 Income = (12826/0.22) = (1282600/22) = 58300. 5. Equate calculated income to given income formula to find z: z + 3300 = 58300 z = 58300 - 3300 = 55000. 6. Calculate 2.5% of z: 2.5% of 55000 = (2.5/100) × 55000 = 25 × 55 = 1375. Quantity I = 1375 Solving Quantity II: 1. Solve for P: 1.2P^2 = 2268750 P^2 = (2268750/1.2) = (22687500/12) = 1890625 2. Take the square root of both sides. P = \pm\sqrt{1890625} P = 1375 or -1375. Quantity II = +1375 or -1375 Comparison: Comparing Quantity I (1375) with Quantity II (1375, -1375): If P = 1375, Quantity I = Quantity II. If P = -1375, Quantity I > Quantity II. Therefore, combining both possibilities, Quantity I \ge Quantity II. Exam Strategy & Shortcut: When finding the square root of a large number ending in 25 like 1890625, you know the root ends in 5. By checking 1300^2 = 1690000 and 1400^2 = 1960000, you can easily deduce the root is exactly 1375 without complex long division methods. Common Pitfall: The most common mistake in banking/aptitude exams involving quadratic variables (P^2 = x) is ignoring the negative root. Concluding P = 1375 only would lead to marking "Quantity-I = Quantity-II", which is incorrect because of the negative possibility. Final Answer: Therefore, the correct answer is Quantity-I ≥ Quantity-II.

Question 2

The price of an article is first increased by 20% and later on decreased by 25% due to reduction in sales. Find the net percentage change in final price of the article.

Accepted Answer

Concept & Formula: When a value undergoes successive percentage changes x and y, the net percentage change is given by the formula: Net % Change = x + y + (xy/100) (Increases are positive, decreases are negative). Step-by-Step Solution: 1. Identify the changes: First change (x) = +20% (increase) Second change (y) = -25% (decrease) 2. Apply the successive percentage formula: Net Change = 20 + (-25) + (20 × (-25)/100) Net Change = -5 + (-500/100) Net Change = -5 - 5 = -10% 3. Interpret the result: A net change of -10% means a 10% decrease. Since 10% decrease is not among the options (20%, 18%, 38%), the correct choice is "None of these". Exam Strategy & Shortcut: Assume the initial price is 100. After 20% increase: 100 \rightarrow 120. After 25% decrease (which is 1/4th): 120 \rightarrow 120 - 30 = 90. Net change = 100 \rightarrow 90, which is a 10% decrease. Common Pitfall: Simply adding the percentages together (+20% - 25% = -5%), which ignores the compounding effect of the successive changes. Final Answer: Therefore, the correct answer is None of these.

Question 3

In a bank, monthly salary of clerks and officers are in the ratio of $3 : 5$. Each clerk contributes 2% and each officer contributes 3 % of his salary to the Welfare Fund. If each officer's contribution is ₹ 210, what will be the clerk's salary?

Accepted Answer

Concept & Percentage of Ratios: When given a percentage of a proportional value, you can express the actual amount as a fraction of the ratio variable to solve for the unknown multiplier. Step-by-Step Solution: 1. Given: Ratio of salaries for clerk to officer is 3 : 5. 2. Let the clerk's salary be 3x and the officer's salary be 5x. 3. Each officer contributes 3% of their salary. 4. Officer's contribution = 3% of 5x = (3/100) × 5x = 0.15x. 5. We are given that the officer's contribution is ₹ 210. 6. Set up the equation: 0.15x = 210. 7. Solve for x: x = (210/0.15) = (21000/15) = 1400. 8. The clerk's salary is 3x = 3 × 1400 = 4200. Exam Strategy & Shortcut: Officer salary = (210/0.03) = 7000. The ratio of clerk to officer salary is 3 : 5. Since 5 parts = 7000, 1 part = 1400. Clerk salary = 3 parts = 3 × 1400 = 4200. This completely avoids decimals containing variables. Common Pitfall: Calculating the clerk's contribution amount instead of the clerk's total salary as requested by the question. Final Answer: Therefore, the correct answer is ₹ 4200.

Question 4

Directions : Study the following table carefully and answer the questions that follow: (Bank P.O., 2011)  Semester Fees (In ₹ thousands) For Five Different Courses In 6 Different Years  | Years | B.Tech | M.Sc. | B.Ed. | M.Phil | Diploma | |---|---|…

Accepted Answer

Concept & Percentage Increase: To find the percentage increase from one period to the next, calculate the difference between the final and initial values, divide by the initial value, and multiply by 100. Percentage Increase = ( \frac{Final Value - Initial Value}{Initial Value} ) × 100 Step-by-Step Solution: 1. Identify Initial Value: The fee for B.Ed in the previous year (2006) is 11.6 (in ₹ thousands). 2. Identify Final Value: The fee for B.Ed in 2007 is 13.9 (in ₹ thousands). 3. Calculate Difference: 13.9 - 11.6 = 2.3 4. Calculate Percentage: ( (2.3/11.6) ) × 100 \approx ( (23/116) ) × 100 \approx 0.1982 × 100 = 19.82% 5. Approximate: 19.82% is approximately 20%. Exam Strategy & Shortcut: Instead of precise division, look at the fraction 2.3 / 11.6. Notice that 11.6 is close to 11.5, and 2.3 × 5 = 11.5. Therefore, the fraction is very close to 1/5, which is exactly 20%. This avoids heavy calculation. Common Pitfall: A common mistake is dividing the difference by the *final* year's value instead of the *base/previous* year's value, which would give 2.3 / 13.9 \approx 16.5%. Always divide by the starting point. Final Answer: Therefore, the correct answer is 20 %.

Question 5

Directions: Study the following table and answer the questions based on it : Number of Candidates Appeared, Qualified And Selected In a Competitive Examination From 5 States Delhi; H.P.; U.P.; Punjab and Haryana Over The Years 2007 To 2011  | Year |…

Accepted Answer

Concept & Formula: The percentage of candidates selected relative to the candidates appeared is calculated using the formula: Percentage = ( \frac{Selected}{Appeared} ) × 100 Step-by-Step Solution: 1. Delhi: ((94/8000)) × 100 = 1.175% 2. H.P.: ((82/7800)) × 100 = 1.051% 3. U.P.: ((78/7500)) × 100 = 1.040% 4. Punjab: ((85/8200)) × 100 = 1.036% 5. Haryana: ((75/6400)) × 100 = 1.171% Comparing the calculated values, Punjab has the lowest percentage (1.036%). Exam Strategy & Shortcut: Instead of calculating full percentages, compare the fractions \frac{Selected}{Appeared}. Notice that all ratios are around 1%. Comparing (78/75) (U.P. scaling) and (85/82) (Punjab scaling) helps quickly narrow down to Punjab being slightly smaller than U.P. Common Pitfall: Using the "Qualified" column instead of the "Appeared" column for the denominator. Always read the question carefully to ensure the correct base is used. Final Answer: Therefore, the correct answer is Punjab.

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