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Class 8 - Ganita Prakash Chapter 1 - Part 5

Class 8 Ganita Prakash Fractions in Disguise

Achievement Test - Part 5

Welcome to Part 5 of the Class 8 Fractions in Disguise Test Module!

In this section, we dive deeper into Commercial Mathematics. We will calculate backward from discounted prices to find the original Cost Price, analyze inflation rates over time, and learn how to extract the base value after a percentage increase. Review the detailed textbook solutions (Pages 19 to 20), test your speed with MCQs, and try the extra practice questions.[cite: 23, 24]

1 Geometry Box Margin Pg 19

If a shopkeeper buys a geometry box for ₹75 and sells it for ₹110, what is his profit margin with respect to the cost?[cite: 23]

Concept:

Profit = $\text{Selling Price (SP)} - \text{Cost Price (CP)}$. Profit Margin = $\frac{\text{Profit}}{\text{Cost Price}} \times 100$.[cite: 23]

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Hint:

Profit = $110 - 75 = 35$.

Calculate $\frac{35}{75} \times 100$. Simplify the fraction by dividing by 5.

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Mistakes to Avoid:

Dividing by Selling Price: $\frac{35}{110} \times 100 \approx 31.8\%$. This is incorrect. Profit margin is calculated against the initial investment (CP).

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Solution:

Cost Price (CP) = ₹75, Selling Price (SP) = ₹110.

Profit = $110 - 75 = 35$

Profit \% = $\frac{35}{75} \times 100$

$= \frac{7}{15} \times 100 = \frac{700}{15}$

$= 46.66\%$

Ans: His profit margin is 46.66%.

🎯 Marking Scheme:
• 1 Mark for Profit (35).
• 1 Mark for equation $\frac{35}{75} \times 100$.
• 1 Mark for final calculation (46.66%).[cite: 23]

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2 Carpenter's Chair Pg 19

I am a carpenter and I make chairs. The cost of materials for a chair is ₹475 and I want to have a profit margin of 50%. At what price should I sell a chair?[cite: 23]

Concept:

Selling Price (SP) = Cost Price + Profit. A 50% profit means the SP is $150\%$ of the CP.[cite: 23]

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Hint:

Calculate $50\%$ of 475. (Divide 475 by 2).

Add that profit back to the 475 base cost.

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Mistakes to Avoid:

Finding the profit and stopping: $475 \div 2 = 237.5$. Do not leave this as your final answer. That is only the profit amount, not the final Selling Price.

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Solution:

Cost Price (CP) = ₹475

Target Profit = $50\%$

Profit Amount = $50\%$ of $475 = \frac{475}{2} = 237.5$

$\text{SP} = \text{CP} + \text{Profit} = 475 + 237.5 = 712.5$

Ans: I should sell it for ₹712.50.

🎯 Marking Scheme:
• 1 Mark for calculating Profit (237.5).
• 1 Mark for calculating SP (712.5).[cite: 23]

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3 Petrol Inflation Pg 19

The petrol price in 2015 was ₹60 and ₹100 in 2025. What is the percentage increase in the price of petrol?[cite: 23]

Concept:

Percentage Increase = $\frac{\text{Increase Amount}}{\text{Original Base Value}} \times 100$. The original base is always the older, starting value.[cite: 23]

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Hint:

Increase = $100 - 60 = 40$.

Calculate $\frac{40}{60} \times 100$. (Simplify $\frac{40}{60}$ to $\frac{2}{3}$).

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Mistakes to Avoid:

Dividing by the new price: $\frac{40}{100} \times 100 = 40\%$. This is incorrect. Growth is measured from where you started (60), not where you ended up.

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Solution:

Original Price = 60, New Price = 100.

Increase = $100 - 60 = 40$

Increase \% = $\frac{40}{60} \times 100$

$= \frac{2}{3} \times 100 = 66.66\%$

Ans: The price increased by 66.66% (Option iv).

🎯 Marking Scheme:
• 1 Mark for calculating the Increase (40).
• 1 Mark for dividing by 60.
• 1 Mark for final calculation (66.66%).[cite: 23]

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4 Elephant Population Pg 20

The population of elephants in a national park increased by 5% in the last decade. If the population of the elephants last decade is $p$, the population now is:
(i) $p \times 0.5$
(iv) $p \times 1.05$[cite: 24]

Concept:

New Population = Base Population + Increase. Since the increase is $5\%$ of $p$, New Population = $p + 0.05p = 1.05p$.[cite: 24]

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Hint:

$100\% + 5\% = 105\%$.

What is $105\%$ expressed as a decimal multiplier?

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Mistakes to Avoid:

Choosing 0.05: $p \times 0.05$ only calculates the *amount* of the increase. It does not give the new *total* population.

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Solution:

Base Population = $p$ ($100\%$)

New Population = $100\% + 5\% = 105\%$

$105\% = \frac{105}{100} = 1.05$

New Population = $p \times 1.05$

Ans: Option (iv) $p \times 1.05$.

🎯 Marking Scheme:
• 1 Mark for selecting Option (iv).[cite: 24]

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5 Backward Variable Calculation Pg 20

A number increased by 20% becomes 90. What is the number?[cite: 24]

Concept:

Let the number be $x$. A $20\%$ increase means $120\%$ of $x = 90$. Set up the equation $1.2x = 90$ and solve for $x$.[cite: 24]

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Hint:

$x \times \frac{120}{100} = 90$.

$x = 90 \times \frac{100}{120} = 90 \times \frac{5}{6}$.

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Mistakes to Avoid:

Decreasing 90 by 20%: Do not calculate $90 - (20\% \text{ of } 90) = 90 - 18 = 72$. The $20\%$ growth happened on the smaller base number, not on 90.

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Solution:

Let original number = $x$.

Increased value = $x + 20\%x = 120\% \text{ of } x$.

$1.2x = 90$

$x = \frac{90}{1.2} = \frac{900}{12}$

$x = 75$

Ans: The original number is 75.

🎯 Marking Scheme:
• 1 Mark for equation $1.2x = 90$.
• 1 Mark for calculating $x = 75$.[cite: 24]

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1 Discount Calculation

A ₹800 jacket is on sale for 25% off. What is the Selling Price?

A. 200

B. 400

C. 600

D. 775

Concept:

A $25\%$ discount means you pay $100\% - 25\% = 75\%$ of the price. Or, find $25\%$ ($\frac{1}{4}$) and subtract it.

Hint:

$25\%$ of $800 = \frac{800}{4} = 200$.

SP = $800 - 200$.

Mistakes to Avoid:

Choosing 200: 200 is the *discount amount*, not the final *Selling Price*.

Solution:

Discount = $25\%$ of $800 = 200$

SP = $800 - 200 = 600$

Ans: Option C (600)

2 Ticket Inflation

A concert ticket price rose from ₹1200 to ₹1500. What is the percentage increase?

A. 20%

B. 25%

C. 30%

D. 300%

Concept:

% Increase = $\frac{\text{Increase}}{\text{Original Base}} \times 100$.

Hint:

Increase = $1500 - 1200 = 300$.

Calculate $\frac{300}{1200} \times 100$.

Mistakes to Avoid:

Dividing by the new price: $\frac{300}{1500} = 20\%$. This is incorrect because you must calculate growth from the starting base.

Solution:

Increase = 300

\% Increase = $\frac{300}{1200} \times 100 = \frac{1}{4} \times 100 = 25\%$

Ans: Option B (25%)

3 Adding GST

A restaurant bill is ₹500. A 5% GST is added. What is the final total?

A. 505

B. 525

C. 550

D. 750

Concept:

Calculate the tax amount ($5\%$ of 500) and add it to the base bill.

Hint:

$10\%$ of 500 is 50. So $5\%$ is 25.

Total = $500 + 25$.

Mistakes to Avoid:

Adding 5 directly: 505 is wrong. 5% means 5 per 100, not 5 absolute currency units.

Solution:

GST = $\frac{5}{100} \times 500 = 25$

Final = $500 + 25 = 525$

Ans: Option B (525)

4 Backward Decrease

A number decreased by 10% becomes 180. What is the original number?

A. 198

B. 200

C. 162

D. 220

Concept:

A $10\%$ decrease means the new number is $90\%$ of the original. $0.9x = 180$.

Hint:

$x = \frac{180}{0.9}$. Divide to find $x$.

Mistakes to Avoid:

Adding 10% to 180: Calculating $180 + 18 = 198$ is the classic percentage trap. The $10\%$ drop was calculated on the *original* number, not on 180.

Solution:

$90\%$ of $x = 180$

$x = \frac{180}{0.9} = \frac{1800}{9} = 200$

Ans: Option B (200)

5 Semantic Decay

"Sales dropped by 40%". This means current sales are what % of original?

A. 40%

B. 60%

C. 140%

D. 2.5%

Concept:

Original is always $100\%$. A drop of $40\%$ leaves $100\% - 40\%$.

Hint:

$100 - 40 = ?$

Mistakes to Avoid:

Answering 40%: "Dropped *to* 40%" means it is 40%. "Dropped *by* 40%" means 40% was removed. Watch the prepositions!

Solution:

Current = $100\% - 40\% = 60\%$

Ans: Option B (60%)

1 Grocery Inflation

The price of a grocery basket went from ₹200 to ₹230 over the year. What is the rate of inflation?

Concept:

Inflation rate = Percentage Increase. $\frac{\text{Increase}}{\text{Original}} \times 100$.

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Hint:

Increase = $230 - 200 = 30$.

Calculate $\frac{30}{200} \times 100$.

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Mistakes to Avoid:

Using the new price: $\frac{30}{230} \approx 13\%$. Inflation is calculated from the base year (200).

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Solution:

Increase = 30

Inflation Rate = $\frac{30}{200} \times 100$

$= \frac{30}{2} = 15\%$

Ans: The rate of inflation is 15%.

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2 Reverse GST Extraction

A laptop costs ₹47,200 *including* an 18% GST. Find the original base price before tax.

Concept:

If a price includes $18\%$ tax, then the final price represents $118\%$ of the original base. $\text{Base} \times 1.18 = \text{Final Price}$.

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Hint:

$\text{Base} = \frac{47200}{1.18} = \frac{4720000}{118}$.

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Mistakes to Avoid:

Subtracting 18% of the final price: Calculating $18\%$ of 47200 (8496) and subtracting it gives 38704. This is completely wrong. The $18\%$ tax was originally calculated on the *base* price, not the final price!

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Solution:

$118\% \text{ of Base} = 47200$

$\text{Base} = 47200 \times \frac{100}{118}$

$\text{Base} = 400 \times 100 = \text{₹}40,000$

Ans: The original base price was ₹40,000.