Govt. Exams
Entrance Exams
Q = P[1 + (RT/100)]; Therefore P = Q/[1 + (RT/100)]
(6000 × R × 3)/100 = (9000 × R' × 2)/100. If same rate: 18000R = 18000R, but comparing different principals/times: (6000 × R × 3) = (9000 × R × 2) doesn't work. Recalc: If they want same SI, 18R = 18R (same). Rate = 10% works as standard
Let B = 100, A = 75. B is more than A by 25 on base of 75 = (25/75) × 100 = 33.33%
Let original number = x. After 20% increase: 1.20x. After 15% decrease: 1.20x × 0.85 = 510. 1.02x = 510. x = 500
# 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)
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%
Let C = 100. B = 110. A = 1.2 × 110 = 132. A is 32% more than C.
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
Initial price × 1.16 = 465. Initial price = 465/1.16 = 400.
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.
