After 15% discount: M × (1 - 0.15) = 500, so M × 0.85 = 500, M = 500/0.85 = ₹588.24 (approximately).
Therefore, option A is correct.
New price = 1.25P. For constant expenditure: New consumption = 1/1.25 = 0.8. Reduction = 20%.
SI = (50,000 × 10 × T)/100. 15,000 = 5000T. T = 3 years.
CP = 100, MP = 180, SP = 144 (for 44% profit). Discount = 180 - 144 = 36. Discount% = (36/180) × 100 = 20%.
Let C = 100. B = 80. A = 100. Wait: B = 80, A = 1.25 × 80 = 100. So A = C. Hmm, let me recalculate: If B is 20% less than C, B = 0.8C. A is 25% more than B, so A = 1.25B = 1.25 × 0.8C = C. So A = C. But answer says B is correct. Let me verify: A = 1.25B, B = 0.8C. A = 1.25 × 0.8C = C. A/C = 1. So A is 0% more. This doesn't match. The answer should be C.
Initial price × 1.16 = 465. Initial price = 465/1.16 = 400.
When two items are sold at the same price but one at profit and another at loss, we use the cost price formula to find the overall profit/loss.
Step 1: Find Cost Price of Item 1 (25% profit)
If selling price is ₹900 at 25% profit, then:
Step 2: Find Cost Price of Item 2 (25% loss)
If selling price is ₹900 at 25% loss, then:
Step 3: Calculate Total Cost Price and Total Selling Price
Step 4: Find Overall Profit/Loss
Selling price (SP) of each item = ₹900
First item: 25% profit
CP
1
=
125
900×100
=₹720
Second item: 25% loss
CP
2
=
75
900×100
=₹1200
Total Cost Price
720+1200=₹1920
Total Selling Price
900+900=₹1800
Loss
1920−1800=₹120
Loss Percentage
1920
120
×100=6.25%
Therefore, the overall result is a loss of 6.25%.
Answer: Overall loss is ₹120 (Option C) ₹120 loss
Let C = 100. B = 110. A = 1.2 × 110 = 132. A is 32% more than C.
For 20% gain at ₹1,200: CP = 1,200/1.20 = ₹1,000. For 20% loss at ₹1,200: CP = 1,200/0.80 = ₹1,500. Total CP = ₹2,500, Total SP = ₹2,400. Loss = ₹100. Loss% = (100/2,500) × 100 = 4%
# Depreciation Problem — Compound Decay
When a value depreciates by a fixed percentage annually, we use the compound depreciation formula: \(V_n = V_0(1 - r)^n\), where \(V_0\) is the initial value, \(r\) is the depreciation rate, and \(n\) is the number of years.
Step 1: Identify the given values
Initial value: \(V_0 = ₹8,00,000\)
Annual depreciation rate: \(r = 15\% = 0.15\)
Time period: \(n = 2\) years
Step 2: Set up the depreciation formula
After each year, the car retains \((1 - 0.15) = 0.85\) of its previous value.
Step 3: Substitute values
Step 4: Calculate step-by-step
First, find \((0.85)^2\):
Then multiply by the initial value:
Answer: The car's value after 2 years will be ₹5,78,000 (Option A)
