Question 1

A trader professes to sell his goods at a nominal gain percentage but actually earns $37 \frac{1}{2}\%$ profit by using false weight. If for a kg he uses a weight of $800$ gm, what is the nominal gain percentage at which he claims to be selling his …

Accepted Answer

Concept & Nominal vs. Actual Profit: A trader's nominal (professed) profit is based on the declared selling price and the assumed standard weight. The actual profit depends on the actual money received compared to the cost of the actual physical weight delivered. Step-by-Step Solution: • Let the cost price (CP) of 1 gm of goods be Re. 1. • Actual Transaction: The trader uses an 800 gm weight for a kilogram (1000 gm). • The actual CP incurred by the trader is for the goods he physically gives away: CP of 800 gm = Rs. 800. • He earns an actual profit of 37 (1/2)%. Convert to fraction: 37.5% = (3/8). • Actual Profit = (3/8) × Actual CP = (3/8) × 800 = Rs. 300. • Actual Selling Price (SP) = Actual CP + Actual Profit = 800 + 300 = Rs. 1100. • Nominal (Professed) Claim: He claims to be selling 1000 gm (which costs Rs. 1000) for the SP of Rs. 1100. • Nominal Profit = SP - Claimed CP = 1100 - 1000 = Rs. 100. • Nominal Gain Percentage = ( \frac{Nominal Profit}{Claimed CP} ) × 100 • Nominal Gain % = (100/1000) × 100 = 10% Exam Strategy & Shortcut: Let professed profit factor be x. The false weight factor is (1000/800) = (5/4) (he gets paid for 5 parts but gives 4). Total profit factor = 1 + 37.5% = 1 + (3/8) = (11/8). Equation: x × (5/4) = (11/8) \implies x = (11/8) × (4/5) = (11/10) = 1.1. A factor of 1.1 means a 10% nominal gain. Common Pitfall: It is easy to confuse the base of the percentages. Ensure that actual profit is calculated on the actual weight delivered (800g), while nominal profit is calculated on the standard weight (1000g). Final Answer: Therefore, the correct answer is 10%.

Question 2

A manufacturer sold a machine to a wholesale dealer at a profit of $10\%$. The wholesale dealer sold it to a retailer at a profit of $20\%$. While transporting some defect occurred in the machine and hence the retailer sold it at a loss of $5\%$. Th…

Accepted Answer

Concept & Chain Rule in Profit and Loss: When an item passes through multiple hands with successive profits and losses, we apply the chain rule of percentages. Final Price = Initial Price × (1 + Profit_1%) × (1 + Profit_2%) × (1 - Loss_3%) SP = CP × ( (100 \pm P/L_1/100) ) × ( (100 \pm P/L_2/100) ) \dots Step-by-Step Solution: • Given: • Profit by manufacturer = 10% • Profit by wholesale dealer = 20% • Loss by retailer = 5% • Final amount paid by customer = ₹ 627 • Let the original cost of the machine for the manufacturer be x. • Apply the successive change multipliers: • x × (1 + (10/100)) × (1 + (20/100)) × (1 - (5/100)) = 627 • x × (110/100) × (120/100) × (95/100) = 627 • x × (11/10) × (6/5) × (19/20) = 627 • x × (1254/1000) = 627 • Solving for x: • x = 627 × (1000/1254) • x = (1000/2) = 500 Exam Strategy & Shortcut: Work with percentage multipliers directly as fractions for faster cancellation: 10% profit = (11/10), 20% profit = (6/5), 5% loss = (19/20). Set up the equation x × (11 × 6 × 19/10 × 5 × 20) = 627. Notice that 11 × 19 = 209, and 209 × 3 = 627. So, x × (3 × 2/1000) = 3 \Rightarrow x = 500. Common Pitfall: A common mistake is adding the percentages together (10 + 20 - 5 = 25%) and calculating the profit on the base price. This ignores the compounding nature of successive transactions. Final Answer: Therefore, the correct answer is ₹ 500.

Question 3

If there is a profit of $20\%$ on the cost price of an article, the percentage of profit calculated on its selling price will be (S.S.C., 2010)

Accepted Answer

Concept & Profit Margin Conversion: Standard profit percentage is calculated on the Cost Price (CP). To find the profit percentage based on the Selling Price (SP), known as the profit margin, we use the formula: Profit on SP % = ( \frac{Profit}{SP} ) × 100 Step-by-Step Solution: • Given: • Actual Profit = 20% on Cost Price. • Let the Cost Price (CP) be 100. • Calculate Profit and Selling Price: • Profit = 20% of 100 = 20. • SP = CP + Profit = 100 + 20 = 120. • Calculate the profit percent calculated on SP: • New Profit % = (\frac{Profit}{SP}) × 100 • New Profit % = ((20/120)) × 100 • New Profit % = ((1/6)) × 100 = 16.66% = 16(2/3)% Exam Strategy & Shortcut: Use fractions. A profit of 20% on CP means a fraction of (1/5). This means Profit = 1 unit, CP = 5 units. SP = CP + Profit = 5 + 1 = 6 units. Profit on SP is \frac{Profit}{SP} = (1/6). The percentage equivalent of (1/6) is universally known as 16(2/3)%. Common Pitfall: A common mistake is assuming profit on SP is always higher or identical to profit on CP. Since SP is generally larger than CP in a profitable transaction, the denominator increases, making the profit percentage on SP mathematically smaller. Final Answer: Therefore, the correct answer is 16(2/3).

Question 4

A man buys an article for $10\%$ less than its value and sells it for $10\%$ more than its value. His gain or loss percent is

Accepted Answer

Concept & Value vs Cost Price: When an article is bought at a discount relative to its "value" and sold at a premium relative to the same "value", the profit percentage must be calculated on the discounted Cost Price, not the baseline value. Step-by-Step Solution: • Given: • Cost Price (CP) = Value - 10% of Value • Selling Price (SP) = Value + 10% of Value • Let the intrinsic Value of the article be 100. • Calculate Cost Price (CP): • CP = 100 - (10% of 100) = 100 - 10 = 90 • Calculate Selling Price (SP): • SP = 100 + (10% of 100) = 100 + 10 = 110 • Calculate actual Gain: • Gain = SP - CP = 110 - 90 = 20 • Calculate Gain Percentage: • Gain % = (\frac{Gain}{CP}) × 100 • Gain % = ((20/90)) × 100 • Gain % = (200/9)% = 22.22% • Evaluate against options: • 22.22% is strictly more than 20%. Exam Strategy & Shortcut: If you buy at a 10% discount and sell at a 10% markup on a base of 100, your CP is 90 and SP is 110. Your absolute profit is 20. If your CP was 100, your profit would be exactly 20%. Since your CP (90) is *less* than 100, dividing the same profit margin (20) by a smaller base mathematically results in a percentage *greater* than 20%. No exact calculation is needed. Common Pitfall: A classic trap is to assume that a 10% drop on purchase and a 10% increase on sale relative to a base value cancel out, or that they sum exactly to a 20% profit. Always normalize back to the actual Cost Price. Final Answer: Therefore, the correct answer is more than 20% profit.

Question 5

A man sells a book at a profit of $20\%$. If he had bought it at $20\%$ less and sold it for ₹ 18 less, he would have gained $25\%$. The cost price of the book is (M.A.T., 2009)

Accepted Answer

Concept & Successive Profit Scenarios: When both Cost Price and Selling Price change, formulate equations for the initial and final states based on CP and SP, and apply the new profit percentage to the new CP. New SP = New CP × (1 + \frac{New Profit %}{100}) Step-by-Step Solution: • Let the original Cost Price be CP = x. • Initial profit is 20%, so original Selling Price SP = 1.2x. • The man bought it at 20% less: New CP = x - 0.2x = 0.8x. • He sold it for ₹ 18 less: New SP = 1.2x - 18. • On this transaction, he gains 25%. So, New SP = New CP × 1.25. • Substitute the expressions: 1.2x - 18 = 0.8x × 1.25 • 1.2x - 18 = 1.0x • 1.2x - x = 18 • 0.2x = 18 • x = (18/0.2) = 90 Exam Strategy & Shortcut: Use a base of 100 units for CP. Let CP = 100u, SP = 120u. New CP = 80u. New Profit = 25% on 80u = 20u. New SP = 80u + 20u = 100u. The decrease in SP is 120u - 100u = 20u. We are given this decrease is ₹ 18. So, 20u = 18. We need CP, which is 100u. 100u = 18 × 5 = 90. Common Pitfall: Applying the new profit percentage (25%) to the original Cost Price instead of the updated, reduced Cost Price. Final Answer: Therefore, the correct answer is ₹ 90.

Question 6

A watch is sold at a profit of $20\%$. If both the cost price and the selling price of the watch are decreased by ₹ 100, the profit would be $5\%$ more. Original cost price of the watch is (A.A.O. Exam, 2010)

Accepted Answer

Concept & Absolute Value Changes in Profit and Loss: When a fixed absolute amount is deducted from both CP and SP, the profit percentage changes. Set up the foundational equation linking the updated CP and SP. Step-by-Step Solution: • Let original CP = x. • Original Profit = 20%, so Original SP = 1.2x. • Both CP and SP decrease by ₹ 100: • New CP = x - 100 • New SP = 1.2x - 100 • The new profit is 5% more, meaning it is 20% + 5% = 25%. • Set up the equation: New SP = New CP × 1.25 • 1.2x - 100 = (x - 100) × 1.25 • 1.2x - 100 = 1.25x - 125 • 1.25x - 1.2x = 125 - 100 • 0.05x = 25 • x = (25/0.05) = (2500/5) = 500 Exam Strategy & Shortcut: Use the ratio method. Initial CP : SP = 100 : 120 = 5 : 6. New Profit = 25%, so New CP : SP = 100 : 125 = 4 : 5. Both decreased by 100. Initial ratio: 5x, 6x. (5x - 100/6x - 100) = (4/5) Cross multiply: 25x - 500 = 24x - 400 \implies x = 100. Original CP = 5x = 5(100) = 500. This avoids decimals entirely. Common Pitfall: Assuming "profit would be 5% more" means the new profit is 5% of CP, rather than interpreting it as the old percentage plus 5% (i.e., 25%). Final Answer: Therefore, the correct answer is ₹ 500.

Question 7

A man sells two articles at ₹ 99 each. He gains $10\%$ on one and loses $10\%$ on the other. Then on overall basis he (P.C.S., 2006)

Accepted Answer

Concept & Absolute Net Loss Calculation: Similar to the previous problem, determine the overall percentage loss first, and then translate that percentage into the actual cash amount lost based on the Total Selling Price. Net Loss % = (x^2/100) Step-by-Step Solution: • Total Selling Price (SP) = ₹ 99 + ₹ 99 = ₹ 198. • Since SPs are identical and percentage gain (10%) equals percentage loss (10%), we find the overall loss percentage. • Net Loss % = (10^2/100) = (100/100) = 1% loss. • This means the Total Selling Price represents 99% (100% - 1%) of the Total Cost Price. • Let Total CP be x. Then 99% of x = 198. • 0.99x = 198 \implies x = (198/0.99) = 200. • The Total Cost Price is ₹ 200, and the Total Selling Price is ₹ 198. • Absolute Loss = Total CP - Total SP = 200 - 198 = 2. • The transaction results in a loss of ₹ 2. Exam Strategy & Shortcut: Use the ratio method. The net loss is 1%, which is (1/100). This means if CP is 100 units, Loss is 1 unit, and SP is 99 units. We know Total SP = 198. If 99 units = ₹ 198, then 1 unit = ₹ 2. The loss is exactly 1 unit, which equals ₹ 2. Common Pitfall: Calculating the 1% loss on the Total Selling Price (taking 1% of 198 = 1.98) instead of recognizing that 198 represents 99% of the original base (Cost Price). Final Answer: Therefore, the correct answer is loses ₹ 2.

Question 8

A man sold two steel chairs for ₹ $500$ each. On one, he gains $20\%$ and on the other, he loses $12\%$. How much does he gain or lose in the whole transaction? (M.A.T., 2006)

Accepted Answer

Concept & Formula: To find the overall profit or loss percentage, we must first calculate the total Cost Price (CP) and total Selling Price (SP). The formula for CP when SP and Profit/Loss percentages are known is: CP = (SP × 100/100 \pm Profit/Loss)% The overall gain percentage is computed as \frac{Total SP - Total CP}{Total CP} × 100. Step-by-Step Solution: • Given: Selling price of each chair (SP_1 = SP_2) = ₹ 500. • Total SP: 500 + 500 = ₹ 1000. • CP of first chair (20% gain): CP_1 = 500 × (100/120) = 500 × (5/6) = (2500/6) = (1250/3). • CP of second chair (12% loss): CP_2 = 500 × (100/88) = 500 × (25/22) = (12500/22) = (6250/11). • Total CP: (1250/3) + (6250/11) = (13750 + 18750/33) = (32500/33). • Overall Gain: Total SP - Total CP = 1000 - (32500/33) = (33000 - 32500/33) = (500/33). • Gain Percentage: \frac{Gain}{Total CP} × 100 = (\frac{500/33)}{(32500/33)} × 100 = (500/32500) × 100 = (20/13)% \approx 1.538%. • Rounding to the nearest half percent gives a 1.5% gain. Exam Strategy & Shortcut: Unlike problems where the gain and loss percentages are equal (where the net result is always a loss of (x^2/100)%), different percentages require finding the exact ratio. Using fractions directly instead of decimals prevents rounding errors mid-calculation. Common Pitfall: A frequent mistake is averaging the percentages: (20 - 12/2) = 4% gain, which is entirely incorrect because the cost prices of the two items are different. Final Answer: Therefore, the correct answer is 1.5% gain.

Question 9

If a person makes a profit of $10\%$ on one-fourth of the quantity sold and a loss of $20\%$ on the rest, then what is the average percent profit or loss? (J.M.E.T., 2004)

Accepted Answer

Concept & Fractional Weighted Average: To find the total percentage profit or loss across an entire quantity, apply the given profit and loss percentages to their respective fractions of the whole. Losses are represented as negative values. Net % = (Fraction_1 × Profit_1) - (Fraction_2 × Loss_2) Step-by-Step Solution: • First Part: One-fourth ((1/4)) of the quantity. • Profit on First Part: 10%. • Second Part: The rest, which is 1 - (1/4) = (3/4) of the quantity. • Loss on Second Part: 20%. • Calculating the net effect: Net % = ((1/4) × 10%) + ((3/4) × -20%) Net % = 2.5% - 15% Net % = -12.5% • The negative sign indicates an overall loss. Exam Strategy & Shortcut: Assume the total cost price is 100 units consisting of 4 equal parts costing 25 each. Part 1 (Cost = 25): +10% of 25 = +2.5 profit. Remaining 3 parts (Cost = 75): -20% of 75 = -15 loss. Net effect = +2.5 - 15 = -12.5. Since the base is 100, the net effect is exactly -12.5%, meaning a 12.5% loss. Common Pitfall: A common error is misinterpreting "the rest". If a quarter is used, the remainder is three-quarters ((3/4)), not a half or some other fraction. Final Answer: Therefore, the correct answer is 12.5% loss.

Question 10

A cloth merchant sold half of his cloth at $20\%$ profit, half of the remaining at $20\%$ loss and the rest was sold at the cost price. In the total transaction, his gain or loss will be

Accepted Answer

Concept & Net Effect via Fractions: To find the total gain or loss percentage, apply the given profit and loss rates to their respective fractions of the total quantity. Losses are treated as negative values, and selling at cost price means a 0% profit. Net Effect % = \sum (Fraction × Rate) Step-by-Step Solution: • Part 1: "Half of his cloth" = (1/2). • Rate = +20% (Profit). • Part 2: "Half of the remaining". • Remaining cloth after first sale = 1 - (1/2) = (1/2). • Half of this remainder = (1/2) × (1/2) = (1/4). • Rate = -20% (Loss). • Part 3: "The rest". • Cloth accounted for so far = (1/2) + (1/4) = (3/4). • The rest = 1 - (3/4) = (1/4). • Rate = 0% (Sold at cost price). • Calculate the Overall Net Effect: Net % = ((1/2) × 20) + ((1/4) × -20) + ((1/4) × 0) Net % = 10 - 5 + 0 Net % = +5% • Since the result is positive, it is a 5% gain. Exam Strategy & Shortcut: Assume the total cloth is 100 meters, costing ₹ 1 per meter (Total CP = ₹ 100). - Sell 50 meters at 20% profit: SP = 50 × 1.2 = ₹ 60. - Sell 25 meters at 20% loss: SP = 25 × 0.8 = ₹ 20. - Sell remaining 25 meters at CP: SP = ₹ 25. Total SP = 60 + 20 + 25 = 105. Gain = 105 - 100 = 5. Since base is 100, gain is exactly 5%. Common Pitfall: A common misinterpretation is reading "half of the remaining" simply as "the other half". It is crucial to mathematically compute fractions sequentially based on what is left over. Final Answer: Therefore, the correct answer is 5% gain.

Question 11

A man bought goods worth ₹ $6000$ and sold half of them at a gain of $10\%$. At what gain percent must he sell the remainder so as to get a gain of $25\%$ on the whole?

Accepted Answer

Concept & Target Average Profit: When a quantity is divided into equal halves, the overall average profit percentage is the simple average of the profit percentages of the two halves. Overall Profit % = \frac{Profit_1% + Profit_2%}{2} Step-by-Step Solution: • Total Cost Price: ₹ 6000. • Target overall gain: 25% on the whole. • Total desired profit = 25% of 6000 = ₹ 1500. • First half: Half of the goods cost ₹ 3000. • Gain on first half = 10% of 3000 = ₹ 300. • Second half: The remaining goods cost ₹ 3000. • Required gain on remainder = Total desired profit - Gain on first half • Required gain = 1500 - 300 = ₹ 1200. • Gain percent on remainder: (1200/3000) × 100 = 40% Exam Strategy & Shortcut: Since the goods are split into two exactly equal halves, you can ignore the ₹ 6000 completely. It is extraneous information. Let the required profit percentage be x. (10% + x%/2) = 25% 10 + x = 50 x = 40 The remainder must be sold at a 40% gain. Common Pitfall: A common error is to directly subtract the percentages (25% - 10% = 15%), failing to realize that the 10% only applies to half the quantity, not the whole. Final Answer: Therefore, the correct answer is 40%.

Question 12

A trader purchases a watch and a wall clock for ₹ 390. He sells them making a profit of 10% on the watch and 15% on the wall clock. He earns a profit of ₹ 51.50. The difference between the original prices of the wall clock and the watch is equal to

Accepted Answer

Concept & Simultaneous Equations: When given the combined cost and combined profit from two different percentage rates, we can set up a system of linear equations to solve for individual variables. Step-by-Step Solution: • Let the original price of the watch be W and the wall clock be C. • Total cost: W + C = 390 (Equation 1) • Total profit from 10% on watch and 15% on clock: 0.10W + 0.15C = 51.50 • Multiply the profit equation by 100 to clear decimals: 10W + 15C = 5150 • Divide by 5 for simpler numbers: 2W + 3C = 1030 (Equation 2) • Multiply Equation 1 by 2: 2W + 2C = 780 (Equation 3) • Subtract Equation 3 from Equation 2: (2W + 3C) - (2W + 2C) = 1030 - 780 \Rightarrow C = 250. • Substitute C back into Equation 1: W = 390 - 250 = 140. • Difference between original prices: C - W = 250 - 140 = 110. Exam Strategy & Shortcut: Use the Percentage Shifting method. If both items were sold at a 10% profit, the total profit would be 10% of 390 = ₹ 39. The extra profit 51.50 - 39 = 12.50 comes purely from the extra 5% profit on the wall clock. So, 5% of C = 12.50 \Rightarrow C = 250. Then W = 140. 250 - 140 = 110. Common Pitfall: Misaligning the percentages with the items or making arithmetic errors when solving the simultaneous equations. Final Answer: Therefore, the correct answer is ₹ 110.

Question 13

A firm of readymade garments makes both men's and women's shirts. Its average profit is 6% of the sales. Its profit in men's shirts average 8% of the sales and women's shirts comprise 60% of the output. The average profit per sales rupee in women's …

Accepted Answer

Concept & Weighted Average: The overall average profit percentage is the weighted average of the profit percentages of the individual categories (men's and women's shirts) based on their sales volume. Total Profit = Profit_{Men} + Profit_{Women} Step-by-Step Solution: • Let the total sales volume (in rupees) be 100x. • The overall average profit is 6% of sales, so Total Profit = 6x. • Women's shirts comprise 60% of the output. Assuming sales value is proportional to output, sales of women's shirts = 60x, and sales of men's shirts = 40x. • The profit on men's shirts is 8% of their sales. Profit on men's shirts = 8% of 40x = 3.2x. • Let the profit on women's shirts be P_w. • Total Profit = Profit on men's shirts + Profit on women's shirts • 6x = 3.2x + P_w • P_w = 6x - 3.2x = 2.8x. • The average profit per sales rupee in women's shirts = \frac{Profit on women's shirts}{Sales of women's shirts}. • (2.8x/60x) = (2.8/60) = (28/600) = (7/150) \approx 0.0466. Exam Strategy & Shortcut: Use the rule of alligation. Let w be the profit percentage of women's shirts. Ratio of men's to women's sales is 40:60 = 2:3. Using alligation on profit percentages: (w - 6/6 - 8) = (2/3) \implies 3w - 18 = -4 \implies 3w = 14 \implies w = 4.66%. As a decimal per rupee, 4.66% is 0.0466. Common Pitfall: Students often forget to convert the final percentage (4.66%) into a "per rupee" decimal value, confusing 4.66 with 0.0466. Final Answer: Therefore, the correct answer is 0.0466.

Question 14

The cost of manufacturing an article rose by 18% as a result of the increase in the cost of raw material. A manufacturer revised the selling price of the article so as to maintain the same profit percentage as before. However, he found that he now g…

Accepted Answer

Concept & Proportionality: When the cost and the selling price increase such that the profit percentage remains constant, the absolute profit amount increases by the exact same percentage as the cost. New Profit = Old Profit × (1 + \frac{Increase %}{100}) Step-by-Step Solution: • Let the initial cost price be C and the initial profit be P. • The profit percentage is fixed at (P/C) × 100. • The cost of manufacturing increases by 18%. To maintain the same profit percentage, the profit amount must also increase by 18%. • The problem states that the new profit is ₹ 9 more than the old profit. • Therefore, 18% of the old profit is exactly equal to this ₹ 9 increase. • 0.18 × P = 9 • P = (9/0.18) = (900/18) = 50. Exam Strategy & Shortcut: Recognize that if the profit percentage is constant, any percentage increase in cost results in the exact same percentage increase in profit. Directly equate 18% of the original profit to ₹ 9. 100% of profit = 9 × ((100/18)) = 50. Common Pitfall: A common mistake is assigning the 18% increase to the overall selling price and attempting complex algebraic setups with unknown cost variables, which consumes unnecessary time. Final Answer: Therefore, the correct answer is ₹ 50.

Question 15

Previously, the manufacturing cost of a product was thrice the cost of raw material. Now the cost of raw material increases in the ratio 5 : 12 and manufacturing cost increases in the ratio of 3 : 5. The previous cost of the product was ₹ 8. What sh…

Accepted Answer

Concept & Proportional Changes: The total cost of a product is the sum of its raw material and manufacturing costs. By using the given initial ratios and total cost, we can find the exact initial values. Ratios of increase are then applied to find the new total cost before calculating the final selling price for a desired profit margin. Total Cost = Raw Material Cost + Manufacturing Cost Selling Price = Total Cost × (1 + \frac{Profit %}{100}) Step-by-Step Solution: • Let the initial cost of raw material be R and manufacturing cost be M. • Given that manufacturing cost was thrice the raw material cost: M = 3R. • Total previous cost = R + M = R + 3R = 4R. • We are given the previous total cost was ₹ 8. So, 4R = 8 \implies R = 2. • Therefore, initial raw material cost R = 2 and initial manufacturing cost M = 6. • The raw material cost increases in the ratio 5 : 12. New raw material cost = 2 × (12/5) = (24/5) = 4.8. • The manufacturing cost increases in the ratio 3 : 5. New manufacturing cost = 6 × (5/3) = 10. • Present total cost = New R + New M = 4.8 + 10 = 14.8. • Desired profit is 25%. • Present selling price = 14.8 × (1 + (25/100)) = 14.8 × 1.25 = 18.5. Exam Strategy & Shortcut: Break the ₹ 8 into a 1:3 ratio mentally (₹ 2 and ₹ 6). A 5:12 ratio increase means the new value is (12/5) of the old. 2 × 2.4 = 4.8. A 3:5 increase means multiplying by (5/3). 6 × (5/3) = 10. Total cost is 14.8. Adding 25% ((1/4)) to 14.8: (14.8/4) = 3.7. 14.8 + 3.7 = 18.5. Common Pitfall: A frequent error is interpreting "increases in the ratio a : b" as adding a fraction, rather than seeing it as the multiplier (b/a) where a represents the old value and b represents the new value. Final Answer: Therefore, the correct answer is ₹ 18.50.

Question 16

Garima purchased a briefcase with an additional 10% discount on the reduced price after deducting 20% on the labelled price. If the labelled price was ₹ 1400, at what price did she purchase the briefcase?

Accepted Answer

Concept & Successive Discounts: When multiple discounts are given successively, each subsequent discount is applied to the new reduced price, not the original labelled price. Final Price = Labelled Price × (1 - (D_1/100)) × (1 - (D_2/100)) Step-by-Step Solution: • Labelled price of the briefcase = ₹ 1400. • First discount is 20% on the labelled price. • Price after first discount = 1400 × (1 - 0.20) = 1400 × 0.80 = 1120. • An additional second discount of 10% is given on this reduced price. • Final purchase price = 1120 × (1 - 0.10) = 1120 × 0.90. • Final purchase price = 1120 × (90/100) = 112 × 9 = 1008. Exam Strategy & Shortcut: Use fractional multipliers for speed. A 20% discount leaves (4/5) of the price. A 10% discount leaves (9/10) of the price. Final Price = 1400 × (4/5) × (9/10) = 1400 × (36/50) = 28 × 36. Since 28 × 36: units digit must be 8 × 6 = 48 \implies 8. Both 1008 and 980 are options, so compute 28 × (30 + 6) = 840 + 168 = 1008. Common Pitfall: Adding the successive discount percentages together (20% + 10% = 30%) and applying it as a single discount to the labelled price, which would incorrectly give 1400 × 0.70 = 980. Final Answer: Therefore, the correct answer is ₹ 1008.

Question 17

A T-shirt bought for ₹ 50 is marked at 8 percent profit and then sold at a 10 percent sales discount on marked price. What is the selling price of the T-shirt?

Accepted Answer

Concept & Markup and Discount: The sequence of operations is to first increase the cost price by the markup percentage to find the marked price, and then decrease the marked price by the discount percentage to find the final selling price. Marked Price = Cost Price × (1 + \frac{Markup %}{100}) Selling Price = Marked Price × (1 - \frac{Discount %}{100}) Step-by-Step Solution: • Cost Price (CP) of the T-shirt = ₹ 50. • It is marked at an 8% profit margin. • Marked Price (MP) = 50 × (1 + (8/100)) = 50 × 1.08 = 54. • It is then sold at a 10% discount on the marked price. • Discount amount = 10% of 54 = 5.4. • Selling Price (SP) = MP - Discount = 54 - 5.4 = 48.6. • Since ₹ 48.6 is not equal to ₹ 48, ₹ 50, or ₹ 52, the correct option is "None of these". Exam Strategy & Shortcut: Use a single compound equation: 50 × 1.08 × 0.90. 1.08 × 0.90 = 0.972. 50 × 0.972 = (100/2) × 0.972 = 48.6. The options are integers, so "None of these" is immediately apparent. Common Pitfall: A common mistake is thinking an 8% markup followed by a 10% discount results in a net 2% loss on the original cost price (50 × 0.98 = 49), ignoring that the discount is calculated on the higher marked price. Final Answer: Therefore, the correct answer is None of these.

Question 18

If the S.P. of ₹ 24 results in a 20% discount on list price, what S.P. would result in a 30% discount on list price?

Accepted Answer

Concept & Direct Proportions: The selling price (S.P.) is directly proportional to the remaining percentage of the list price after a discount. You can equate the ratios of S.P. to their corresponding percentages to find the unknown value directly. \frac{SP_1}{100 - Discount_1} = \frac{SP_2}{100 - Discount_2} Step-by-Step Solution: • Let the list price of the article be L. • A 20% discount means the Selling Price is 100% - 20% = 80% of the list price. • We are given that this initial S.P. is ₹ 24. • 80% of L = 24 \implies 0.80 × L = 24. • L = (24/0.80) = (240/8) = 30. • The list price is ₹ 30. • We need to find the new S.P. for a 30% discount. • A 30% discount leaves 100% - 30% = 70% of the list price. • New S.P. = 70% of 30. • New S.P. = 0.70 × 30 = 21. Exam Strategy & Shortcut: Skip finding the list price entirely by using proportion. ₹ 24 represents 80% of the total. We want to find what represents 70% of the total. New S.P. = 24 × ((70/80)) = 24 × ((7/8)) = 3 × 7 = 21. Common Pitfall: Calculating the 30% discount directly on the first selling price of ₹ 24 instead of recognizing that all discounts must be evaluated against the base list price. Final Answer: Therefore, the correct answer is ₹ 21.

Question 19

A sells a scooter priced at ₹ $36000$. He gives a discount of $8\%$ on the first ₹ $20000$ and $5\%$ on the next ₹ $10000$. How much discount can he afford on the remaining ₹ $6000$ if he is to get as much as when $7\%$ discount is allowed on the to…

Accepted Answer

Concept & Strategy: This problem is about weighted averages and total discount matching. The total monetary discount allowed must remain constant regardless of whether it is calculated as a flat rate on the total amount or as a sum of variable rates on partial amounts. Total Target Discount = D_1(Part_1) + D_2(Part_2) + D_3(Part_3) Step-by-Step Solution: • Given: • Total Price = ₹ 36000 • Target overall discount = 7% on ₹ 36000 • Discount 1 = 8% on ₹ 20000 • Discount 2 = 5% on ₹ 10000 • Remaining amount = ₹ 6000 • Calculation: • First, calculate the total target discount amount: 7% of 36000 = (7/100) × 36000 = ₹ 2520. • Next, calculate the discount already given on the first part: 8% of 20000 = (8/100) × 20000 = ₹ 1600. • Calculate the discount given on the second part: 5% of 10000 = (5/100) × 10000 = ₹ 500. • Find the total discount given so far: 1600 + 500 = ₹ 2100. • Determine the remaining discount needed to hit the target: 2520 - 2100 = ₹ 420. • Find what percentage this remaining discount is of the remaining ₹ 6000: Discount % = ((420/6000)) × 100 = 7%. Exam Strategy & Shortcut: You can use the method of deviation (weighted averages). The total needs to balance out to a 7% average. First ₹ 20,000 (Weight 20) is at 8% (+1% deviation). Total surplus = 20 × 1 = +20. Next ₹ 10,000 (Weight 10) is at 5% (-2% deviation). Total deficit = 10 × (-2) = -20. The deviations cancel each other out (+20 - 20 = 0). Since the deviation is currently zero, the remaining part (Weight 6) must exactly match the target average of 7% to keep the overall average at 7%. Common Pitfall: A common mistake is attempting to average the percentages directly (e.g., (8+5+x)/3 = 7) without accounting for the fact that they apply to different principal amounts. Always use absolute monetary values or weighted averages. Final Answer: Therefore, the correct answer is 7%.

Question 20

After successive discounts of $12\%$ and $5\%$ an article was sold for ₹ $209$. What was the original price of the article?

Accepted Answer

Concept & Formula: To find the original Marked Price (MP) given the final Selling Price (SP) and multiple successive discounts, reverse the percentage reductions using multipliers. MP = \frac{SP}{(1 - (d_1/100)) × (1 - (d_2/100))} Step-by-Step Solution: • Given: • Selling Price = ₹ 209 • First discount = 12% • Second discount = 5% • Calculation: • Let the original price be x. • x × (1 - 0.12) × (1 - 0.05) = 209 • x × 0.88 × 0.95 = 209 • 0.88 × 0.95 = 0.836. So, x × 0.836 = 209. • x = (209/0.836) = (209000/836) = 250. Exam Strategy & Shortcut: Calculate the single equivalent discount: 12 + 5 - (12 × 5)/100 = 17 - 0.6 = 16.4%. This means the selling price is (100 - 16.4)% = 83.6% of the original price. 83.6% = 209 \Rightarrow 1% = (209/83.6) = 2.5. Thus 100% = 250. Common Pitfall: Attempting to add the discounts (12 + 5 = 17%) and saying the price is 83% of the original, which gives an incorrect original price of roughly 251.8. Final Answer: Therefore, the correct answer is ₹ 250.

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