The price of a laptop was increased by 20% and then decreased ... | Stage I (CBT I) MCQ | Examoogle

Stage I (CBT I)RRB ALP CBT-I 11 Mar, 2026 Shift 1

The price of a laptop was increased by 20% and then decreased by 30%. If the final price is ₹16,800, what was the original price (in ₹)?

A) $20000$

B) $25000$

C) $22000$

D) $18000$

Correct Answer

📚 GK • GK Ratio MethodStage I (CBT I)RRB ALP CBT-I 11 Mar, 2026 Shift 1

Option A

$20000$

Quick Summary:

Given: Initial price changes: Increased by 20%, then decreased by 30%. Final price = ₹16,800.

📐MAMath SolutionRatio Method

📋 Given

Initial price changes: Increased by 20%, then decreased by 30%. Final price = ₹16,800.

🔢 Formula Used

Final Price=Original Price×(1+x100)×(1−y100)\text{Final Price} = \text{Original Price} \times \left(1 + \frac{x}{100}\right) \times \left(1 - \frac{y}{100}\right)Final Price=Original Price×(1+100x​)×(1−100y​)

⚡ Exam Hall Shortcut / Speed Trick

Use effective percentage or ratios: $+20\% = \frac{6}{5}$ and $-30\% = \frac{7}{10}$ . Overall factor = $\frac{6}{5} \times \frac{7}{10} = \frac{42}{50} = \frac{21}{25}$ . So, $21\text{ units} = 16800 \implies 1\text{ unit} = 800$ . Thus, $25\text{ units} = 25 \times 800 = 20000$ .

⚠️ Common Student Trap / Pitfall

Adding percentages directly ( $+20\% - 30\% = -10\%$ ) instead of applying successive multiplicative changes, leading to an incorrect original price calculation of $16800 / 0.9 = 18666.67$ .

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Define the Variable and Percentage Multipliers

Let the original price of the laptop be $P$ . An increase of $20\%$ increases the value to $100\% + 20\% = 120\%$ of $P$ , and a subsequent decrease of $30\%$ reduces the intermediate price to $100\% - 30\% = 70\%$ .

Multiplier1=1+20100=1.2,Multiplier2=1−30100=0.7\text{Multiplier}_1 = 1 + \frac{20}{100} = 1.2, \quad \text{Multiplier}_2 = 1 - \frac{30}{100} = 0.7Multiplier1​=1+10020​=1.2,Multiplier2​=1−10030​=0.7

Set Up the Successive Price Equation

Multiply the original price by both successive factors to equal the final price of $₹16,800$ .

P×1.2×0.7=16800P \times 1.2 \times 0.7 = 16800P×1.2×0.7=16800

Calculate the Combined Multiplier

Multiply the two percentage factors to find the overall fraction of the original price remaining.

1.2×0.7=0.84  ⟹  0.84P=168001.2 \times 0.7 = 0.84 \implies 0.84 P = 168001.2×0.7=0.84⟹0.84P=16800

Solve for the Original Price

Divide the final price by $0.84$ to determine $P$ .

P=168000.84=16800×10084=20000P = \frac{16800}{0.84} = \frac{16800 \times 100}{84} = 20000P=0.8416800​=8416800×100​=20000

✅

A is correct because the successive multiplier of $1.20 \times 0.70 = 0.84$ gives an original price of $₹16,800 / 0.84 = ₹20,000$ .

Core Concepts Used

Click any tag to open in AI Tutor

Successive Percentage Changes Effective Multipliers Ratio Method for Percentages

💡 EXAM TIP

Successive percentage changes follow the net effect formula $x + y + \frac{xy}{100}\%$ . Here, $+20 - 30 + \frac{(20)(-30)}{100} = -10 - 6 = -16\%$ , which means the final price is $84\%$ of the original.

Discussion (0)

Loading discussion...

Prev Next

Correct Answer

Related Questions

Discussion (0)