Question 1

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 2

Applied to a bill for ₹ $1,00,000$, the difference between a discount of $40\%$ and two successive discounts of $36\%$ and $4\%$ is

Accepted Answer

Concept & Logic: The difference between a single discount (x + y)% and two successive discounts of x% and y% is exactly the interaction term (x × y/100)%. Difference % = (x × y/100)% Step-by-Step Solution: • Given: • Bill amount = ₹ 1,00,000 • Single discount = 40% • Successive discounts = 36% and 4% • Calculation: • Equivalent discount for 36% and 4% = 36 + 4 - (36 × 4/100) = 40 - 1.44 = 38.56%. • Difference in discount percentage = 40% - 38.56% = 1.44%. • Calculate the actual monetary difference: 1.44% of 1,00,000 = (1.44/100) × 100000 = 1440. Exam Strategy & Shortcut: Bypass calculating the full equivalent discount. Since the single discount 40% is the exact sum of 36% and 4%, the difference is simply the product divided by 100: (36 × 4/100) = 1.44%. Directly compute 1.44% of ₹ 1,00,000 to get 1440. Common Pitfall: Assuming that a single discount of 40% is equal to successive discounts of 36% and 4%, which would lead to choosing "Nil". Final Answer: Therefore, the correct answer is ₹ 1440.

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