Question 1

A bag has coins of 50 paisa, 25 paisa and 10 paisa in the respective ratio of 5 : 8 : 3 whose total value is ₹ 144. Find the number of 50 paisa coins.

Accepted Answer

Concept & Value of Coins: When given the ratio of the number of coins of different denominations and their total value, express the total value in terms of a common variable. Total Value = \sum (Number of Coins × Denomination Value) Step-by-Step Solution: • Given: Ratio of coins = 5 : 8 : 3. Total value = ₹ 144. Denominations = 50p (₹ 0.50), 25p (₹ 0.25), and 10p (₹ 0.10). • Let the number of 50 paisa, 25 paisa, and 10 paisa coins be 5x, 8x, and 3x respectively. • Calculate the value contributed by each type of coin in Rupees: • Value of 50p coins = 5x × 0.50 = 2.5x • Value of 25p coins = 8x × 0.25 = 2.0x • Value of 10p coins = 3x × 0.10 = 0.3x • Sum these values to equal the total amount given: • 2.5x + 2.0x + 0.3x = 144 • 4.8x = 144 • Solve for x: • x = (144/4.8) = (1440/48) = 30 • We need the number of 50 paisa coins, which is 5x: • Number of 50p coins = 5 × 30 = 150 Exam Strategy & Shortcut: Work entirely in paise to avoid decimals. The values per x proportion become 5 × 50 = 250, 8 × 25 = 200, and 3 × 10 = 30. Total parts = 250 + 200 + 30 = 480. The total amount is 144 × 100 = 14400 paise. 1 part = (14400/480) = 30. Number of 50p coins = 5 × 30 = 150. Common Pitfall: A frequent error is adding the ratios directly as if they represent the value (e.g., 5x + 8x + 3x = 144). You must multiply the ratio by the respective denomination first. Final Answer: Therefore, the correct answer is 150.

Question 2

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 3

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 4

At the start of a game of cards, J and B together had four times as much money as T, while T and B together had three times as much as J. At the end of the evening, J and B together had three times as much money as T, while T and B together had twic…

Accepted Answer

Concept & Tracking Shares of a Total: To find a win/loss fraction, calculate the player's initial fraction of the total pool and their final fraction of the total pool, then find the difference. Difference = Final Fraction - Initial Fraction Step-by-Step Solution: • Let the total money be M. • Find J's starting fraction: T and B together had three times as much as J. • T + B = 3J. Since J + B + T = M, substituting gives 3J + J = M \Rightarrow 4J = M \Rightarrow J_{start} = (M/4). • Find J's ending fraction: At the end, T and B together had twice as much as J. • T + B = 2J. Substituting into the total gives 2J + J = M \Rightarrow 3J = M \Rightarrow J_{end} = (M/3). • Calculate the difference: J's money changed from (1/4) of the total to (1/3) of the total. • Change = J_{end} - J_{start} = (M/3) - (M/4). • Find a common denominator (12): (4M/12) - (3M/12) = (M/12). • Because the ending fraction is larger than the starting fraction, J won (1/12) of the total money. Exam Strategy & Shortcut: Use the rule (A+B) = k × C \Rightarrow C = (1/k+1) of the total. Start: T+B = 3J \Rightarrow J is (1/4). End: T+B = 2J \Rightarrow J is (1/3). The difference is (1/3) - (1/4) = (1/12). Since (1/3) > (1/4), it is a win. Common Pitfall: Confusing the ratios and calculating for the wrong person, or assuming the total money M changed during the game (it remains constant in closed-system card games). Final Answer: Therefore, the correct answer is Won 1/12.

Question 5

Directions : Study the given table carefully and answer the questions that follow : Number of candidates appeared and qualified for a test (in hundreds) in 6 different years from 5 different zones. (Bank P.O., 2011)  | Year | P App. | P Qual. | Q Ap…

Accepted Answer

Concept & Ratios: A ratio compares two quantities by division. To find the ratio of A to B, simply write it as a fraction A / B and simplify it to its lowest terms. Ratio = \frac{Value A}{Value B} Step-by-Step Solution: 1. Identify Value A: Number of candidates appeared from zone P in 2005. From the table, P (App.) in 2005 is 3.2. 2. Identify Value B: Number of candidates qualified from zone S in 2007. From the table, S (Qual.) in 2007 is 5.6. 3. Form Ratio: Ratio = (3.2/5.6) 4. Simplify: Multiply both numerator and denominator by 10 to remove decimals, resulting in (32/56). Both numbers are divisible by 8. (32 \div 8/56 \div 8) = (4/7) Exam Strategy & Shortcut: When you see 3.2 and 5.6, immediately recognize them as multiples of the 8 times table (8 × 4 = 32 and 8 × 7 = 56). This lets you bypass writing out the fraction and directly select 4 : 7. Common Pitfall: Pulling the wrong data points (e.g., taking P qualified instead of appeared, or S appeared instead of qualified) is the most common error in matrix table lookups. Always double-check column headers. Final Answer: Therefore, the correct answer is 4 : 7.

Question 6

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 7

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 Derivation: To find the required ratio, determine the exact values for Company B in the specified years using the proportions provided in the table linked to the absolute values in the graph. Step-by-Step Solution: • Step 1: Find Production of Company B in 2006 • The graph shows Company A's production in 2006 is 750 tonnes. • The table shows the ratio of Production (A : B) in 2006 is 5 : 4. • Production of Company B in 2006 = ((750/5)) × 4 = 150 × 4 = 600 tonnes. • Step 2: Find Production of Company B in 2008 • The graph shows Company A's production in 2008 is 600 tonnes. • The table shows the ratio of Production (A : B) in 2008 is 3 : 4. • Production of Company B in 2008 = ((600/3)) × 4 = 200 × 4 = 800 tonnes. • Step 3: Calculate the Ratio • Required Ratio = Production B in 2006 : Production B in 2008 • Ratio = 600 : 800. • Simplify by dividing both by 200: • Ratio = 3 : 4. Exam Strategy & Shortcut: Calculate the multipliers directly. In 2006, the multiplier for the ratio is (750/5) = 150. So, B is 150 × 4. In 2008, the multiplier is (600/3) = 200. So, B is 200 × 4. The ratio is simply (150 × 4) : (200 × 4), which immediately simplifies to 150 : 200 or 3 : 4. Common Pitfall: A frequent error is misreading the years or using the sales ratio instead of the production ratio, which would yield entirely different intermediate values and an incorrect final ratio. Final Answer: Therefore, the correct answer is 3 : 4.

Question 8

Directions: The following table gives the percentage distribution of population of five states, P, Q, R, S and T on the basis of poverty line and also on the basis of sex. Study the table and answer the questions based on it.  | State | Percentage o…

Accepted Answer

Concept & Algebraic Ratios: To find the ratio of their total populations, calculate the absolute total population for each state separately by scaling up from the given specific demographic segments. Total Pop = \frac{Segment Population}{% in Category × Demographic Fraction} Step-by-Step Solution: 1. Find Total Population of State Q (Let it be Q_{pop}): - % below poverty line = 25%. - Male fraction below poverty = (3/3+5) = (3/8). - Q_{pop} × 0.25 × ((3/8)) = 2.4 - Q_{pop} × ((1/4)) × ((3/8)) = 2.4 \Rightarrow Q_{pop} × ((3/32)) = 2.4 - Q_{pop} = (2.4 × 32/3) = 0.8 × 32 = 25.6 million. 2. Find Total Population of State T (Let it be T_{pop}): - % below poverty line = 15%. - Male fraction below poverty = (5/5+3) = (5/8). - T_{pop} × 0.15 × ((5/8)) = 6 - T_{pop} × ((0.75/8)) = 6 \Rightarrow T_{pop} = (48/0.75) = (4800/75) = 64 million. 3. Calculate Ratio Q_{pop} : T_{pop}: - Ratio = 25.6 : 64 - Multiply both sides by 10: 256 : 640 - Divide both by 64: 4 : 10 - Simplify: 2 : 5. Exam Strategy & Shortcut: Instead of calculating the actual populations, set up the ratio fractionally to cancel common factors immediately: \frac{Q_{pop}}{T_{pop}} = ( \frac{2.4/0.25 × (3/8)) }{ (6/0.15 × (5/8)) } = ( 2.4 × 8 × 0.15 × 5 / 6 × 8 × 0.25 × 3 ) The 8s cancel out: (2.4 × 0.75/6 × 0.75) = (2.4/6) = (24/60) = (2/5) Common Pitfall: A common mistake is fully calculating large numbers and making an arithmetic error during division (like 4800/75). Leveraging the direct ratio formula (Strategy section) inherently avoids messy division. Final Answer: Therefore, the correct answer is 2 : 5.

Question 9

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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