Question 1

Express 50 paise: ₹ 4 in its simplest form. [ESIC—UDC Exam, 2016]

Accepted Answer

Concept & Unit Conversion: To compare two quantities in a ratio, they must be converted to the same unit of measurement. Step-by-Step Solution: • Given: 50 paise and ₹ 4. • Convert the larger unit (Rupees) to the smaller unit (paise) to avoid decimals. • 1 Rupee = 100 paise. • Therefore, ₹ 4 = 4 × 100 = 400 paise. • Now, set up the ratio using the same units: 50 paise : 400 paise. • Simplify the ratio by dividing both sides by 50: • 50 / 50 : 400 / 50 = 1 : 8. Exam Strategy & Shortcut: Recognize that ₹ 1 is exactly twice 50 paise. Therefore, ₹ 4 is 4 × 2 = 8 times 50 paise. The ratio is immediately 1 : 8. Common Pitfall: Forgetting to convert the units and just taking the ratio of the numbers as they appear (50 : 4 = 25 : 2) is a very common trap. Final Answer: Therefore, the correct answer is 1 : 8.

Question 2

A movie was screened for 3 days – Monday, Tuesday and Wednesday. The respective ratio between the number of spectators on Monday. Tuesday and Wednesday was 2 : 3 : 5 and the price charged for three days was in the respective ratio 2 : 3 : 4. If the …

Accepted Answer

Concept & Proportional Revenue: The total amount earned is the product of the number of spectators and the ticket price. When working with ratios, we can introduce variables to find the exact algebraic amounts. Revenue = Number of Spectators × Price per Ticket Step-by-Step Solution: • Given: • Spectators ratio (Mon:Tue:Wed) = 2 : 3 : 5. Let the actual numbers be 2x, 3x, and 5x. • Price ratio (Mon:Tue:Wed) = 2 : 3 : 4. Let the actual prices be 2y, 3y, and 4y. • Calculate the revenue for each day: • Monday = 2x × 2y = 4xy • Tuesday = 3x × 3y = 9xy • Wednesday = 5x × 4y = 20xy • We are given that the difference between Wednesday and Tuesday's earnings is Rs. 8800: • 20xy - 9xy = 8800 • 11xy = 8800 • xy = 800 • Find the total amount earned over all three days: • Total = 4xy + 9xy + 20xy = 33xy • Substitute the value of xy: • Total = 33 × 800 = 26400. Exam Strategy & Shortcut: You do not need to separate x and y. Treat xy as a single unit block. The revenue ratios are directly (2×2) : (3×3) : (5×4) = 4 : 9 : 20. The difference between Wed and Tue is 20 - 9 = 11 units. 11 units = 8800, so 1 unit = 800. Total units = 4 + 9 + 20 = 33. Total revenue = 33 × 800 = 26400. Common Pitfall: A common mistake is assuming the multipliers for spectators and prices are the same variable (x), which would lead to incorrect squared terms. They are independent ratios. Final Answer: Therefore, the correct answer is ₹ 26400.

Question 3

Directions: Study the following information and answer the questions that follow :  The graph given below represents the production (in tonnes) and sales (in tonnes) of Company A from 2006 to 2011.  [Graph Data of Company A] | Year | Production (in …

Accepted Answer

Concept & Ratio of Aggregates: Calculate the sum of all values in the first set and the sum of all values in the second set independently, then express their relation in simplest fractional form. Ratio = \frac{\sum Production_A}{\sum Sales_A} Step-by-Step Solution: • Calculate the total production of Company A across all years: • Total Production = 750 + 800 + 600 + 550 + 700 + 650 = 4050 tonnes. • Calculate the total sales of Company A across all years: • Total Sales = 300 + 550 + 450 + 400 + 500 + 550 = 2750 tonnes. • Form the ratio of Total Production to Total Sales: • Ratio = 4050 : 2750. • Simplify by dividing both sides by 10: 405 : 275. • Simplify further by dividing both sides by 5: • 405 \div 5 = 81 • 275 \div 5 = 55 • The final simplified ratio is 81 : 55. Exam Strategy & Shortcut: End digits ending in zero make for quick addition. Once you establish the initial ratio of 4050 : 2750, dropping the zero leaves 405 : 275. Since both end in 5, dividing by 5 immediately gives 81 : 55, circumventing more complex simplification tests. Common Pitfall: A common pitfall is reversing the order requested in the prompt (finding Sales to Production instead of Production to Sales), or making arithmetic errors when summing the six data points. Final Answer: Therefore, the correct answer is 81 : 55.

Question 4

Directions: Study the table and answer the given questions.  | Months | Gross Revenue | Amount Allocated for Commission | Amount Allocated for discount and offer | Net Revenue | |---|---|---|---|---| | March | ₹ 360000 | ₹ 31200 | — | — | | April | …

Accepted Answer

Concept & Formula: Use the given ratio to find the missing commission amount, and then calculate the Gross Revenue by summing up all the components. Gross Revenue = Net Revenue + Commission + Discount Step-by-Step Solution: 1. Given for May: - Discount = ₹ 36000 - Ratio of Commission to Discount = 4 : 3 2. Calculate Commission: - Let Commission be 4x and Discount be 3x. - 3x = 36000 \implies x = 12000 - Commission = 4 × 12000 = 48000 3. Calculate Gross Revenue: - Gross Revenue = 336000 (Net) + 48000 (Commission) + 36000 (Discount) - Gross Revenue = 420000 Exam Strategy & Shortcut: Notice that 3 units = 36k, so 1 unit = 12k. The commission is 4 units = 48k. Simply add 336k + 48k + 36k = 420k. Common Pitfall: Reversing the ratio (e.g., treating the commission as 3 parts instead of 4) will result in calculating the wrong commission and subsequently the wrong Gross Revenue. Final Answer: Therefore, the correct answer is ₹ 420000.

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