The price of a machine increased by 10% in the first year, the... | Mathematics MCQ | Examoogle

Examoogle • User • info@examoogle.com • EE-2024-8821

Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked

MathematicsArithmetic

The price of a machine increased by 10% in the first year, then decreased by 20% in the second year, and increased again by 25% in the third year. If the original price was ₹80,000, what is the final price after these three changes?

82,000

85,000

88,000

90,000

Correct Answer

⚙️ TE • Technical Ratio MethodMathematicsArithmetic

Option C

88,000

Quick Summary:

Use the Ratio Method: Convert percentages to fractions (11/10, 4/5, 5/4). Multiply original price by the product of these ratios: $80,000 \times (11/10) \times (4/5) \times (5/4) = 80,000 \times (11/10) = 88,000$ .

🎯

Crack Arithmetic with Examoogle SuperTeachers

Get Free Demo Classes & Live Mocks →

📐MAMath SolutionRatio Method

📋 Given

Original Price = ₹80,000. Successive percentage changes: +10% (1st year), -20% (2nd year), +25% (3rd year).

🔢 Formula Used

Pfinal=Poriginal×(1+r1100)×(1−r2100)×(1+r3100)P_{final} = P_{original} \times \left(1 + \frac{r_1}{100}\right) \times \left(1 - \frac{r_2}{100}\right) \times \left(1 + \frac{r_3}{100}\right)Pfinal​=Poriginal​×(1+100r1​​)×(1−100r2​​)×(1+100r3​​)

⚡ Exam Hall Shortcut / Speed Trick

⚠️ Common Student Trap / Pitfall

Students often incorrectly add or subtract percentages directly (10% - 20% + 25% = 15%) instead of applying successive changes, which leads to wrong answers.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Convert percentage changes to multipliers

Convert the percentage values into multiplication factors: +10% becomes $1 + 0.10 = 1.1$ , -20% becomes $1 - 0.20 = 0.8$ , and +25% becomes $1 + 0.25 = 1.25$ .

1.1×0.8×1.25=1.11.1 \times 0.8 \times 1.25 = 1.11.1×0.8×1.25=1.1

Calculate the final price

Multiply the original price of $80,000$ by the combined multiplier calculated in the previous step.

80,000×1.1=88,00080,000 \times 1.1 = 88,00080,000×1.1=88,000

✅

C is correct because the successive application of the percentage changes $1.1$ , $0.8$ , and $1.25$ on the initial amount of $80,000$ results in a final value of $88,000$ .

Core Concepts Used

Click any tag to open in AI Tutor

Successive Percentage Change Multiplicative Factors Fractional Ratios

💡 EXAM TIP

This concept of compounding is identical to Compound Interest calculations, where the percentage changes act as annual interest rates.

Was this solution helpful?

⚡ Practice on Android App · 4.8 ★

Solve 10,000+ More Questions with AI Tutor

Get instant step-by-step AI explanations, full shift Previous Year Papers (SSC GD, RRB, SSC JE), and regional rank analysis on the official Examoogle App.

Free Download • 100K+ Aspirants

Discussion (0)

Loading discussion...

Prev Next

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Related Questions

Discussion (0)