A company’s profit decreased by $15\%$ each year from ... | Mathematics MCQ | Examoogle

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A company’s profit decreased by $15\%$ each year from 200000. What will be the profit after four years?

109290.25

108290.25

104401.25

116290.25

Correct Answer

⚙️ TE • Technical Direct FormulaMathematicsArithmetic

Option C

104401.25

Quick Summary:

Use the ratio method: 15% decrease means the profit becomes 85% or 17/20 of the previous year's value. Calculate $200000 \times (17/20)^4 = 200000 \times (83521 / 160000) = 1.25 \times 83521 = 104401.25$ .

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📐MAMath SolutionDirect Formula

📋 Given

Initial profit P = 200000, rate of decrease r = 15% per year, and time period n = 4 years.

🔢 Formula Used

A=P×(1−r100)nA = P \times \left(1 - \frac{r}{100}\right)^nA=P×(1−100r​)n

⚡ Exam Hall Shortcut / Speed Trick

⚠️ Common Student Trap / Pitfall

Many students mistake simple interest depreciation for compound depreciation; ensure you apply the exponent of 4 to the multiplier, not just multiplying by 4.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Define variables

Identify the initial principal $P = 200000$ , the annual decrease rate $r = 15\%$ , and the duration $n = 4$ .

P=200000,r=15%,n=4P = 200000, r = 15\%, n = 4P=200000,r=15%,n=4

Set up the compound depreciation formula

Since the profit decreases successively each year, we use the formula for exponential decay.

A=200000×(1−15100)4A = 200000 \times \left(1 - \frac{15}{100}\right)^4A=200000×(1−10015​)4

Simplify the base value

Convert the percentage to a fraction: $1 - 0.15 = 0.85$ or $85/100 = 17/20$ .

A=200000×(1720)4A = 200000 \times \left(\frac{17}{20}\right)^4A=200000×(2017​)4

Calculate the final result

Evaluate the power: $(17/20)^4 = 83521 / 160000$ . Multiplying this by 200000 gives $200000 \times 0.52200625 = 104401.25$ .

A=200000×83521160000=104401.25A = 200000 \times \frac{83521}{160000} = 104401.25A=200000×16000083521​=104401.25

✅

C is correct because calculating the successive decrease of 15% over 4 years on 200000 results in 104401.25.

Core Concepts Used

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Compound Depreciation Exponential Decay Successive Percentage Decrease

💡 EXAM TIP

This same logic applies to calculating the depreciated value of fixed assets (like machinery) in Accounting or the population decline of bacteria in Biology.

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