Class 8 - Ganita Prakash Chapter 1 - Part 4
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Class 8 Ganita Prakash Fractions in Disguise
Achievement Test - Part 4
PROPORTIONS, PROFIT & LOSS Chapter Achievement Test 1.1 C.P. S.P. PROFIT = S.P. > C.P. Part 4: Commercial Mathematics
Welcome to Part 4 of the Class 8 Fractions in Disguise Test Module!

In this section, we transition into Commercial Mathematics. We will use percentages to compare test scores fairly, analyze ingredient proportions in food, and compute Profit & Loss relative to Cost Price (CP) and Selling Price (SP). Review your detailed textbook solutions (Pages 14 to 17), master the MCQs, and conquer the extra practice questions.[cite: 18, 19, 20, 21]
1 Comparing Test Scores Pg 14
Eesha scored 42 marks out of 50 on an English test and 70 marks out of 80 in a Science test. She thinks she did better in English because she only lost 8 marks (compared to 10 in Science). Is she correct? Use percentages to find out.[cite: 18]
Concept:
1
When comparing scores with different maximum marks, you cannot just look at the raw marks lost or gained. You must convert both to a common base—percentages—to make a fair comparison.[cite: 18]
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Hint:
1
Calculate English %: $\frac{42}{50} \times 100$.
2
Calculate Science %: $\frac{70}{80} \times 100$.
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Mistakes to Avoid:
!
Comparing absolute losses: Eesha's logic of "I lost 8 vs 10" is flawed because losing 8 out of 50 is a much larger proportional loss than losing 10 out of 80.
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Solution:
1. English Score:
Percentage = $\frac{42}{50} \times 100$
$= 42 \times 2 = 84\%$

2. Science Score:
Percentage = $\frac{70}{80} \times 100$
$= \frac{7}{8} \times 100 = 7 \times 12.5 = 87.5\%$

Since $87.5\% > 84\%$, she performed better in Science.

Ans: No, Eesha is incorrect. She did better in Science.
🎯 Marking Scheme:
• 1 Mark for English % (84%).
• 1 Mark for Science % (87.5%).
• 1 Mark for the correct conclusion.[cite: 18]
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2 Badam Mix Sugar Comparison Pg 15
Two badam drink mixes have different sugar contents. DEF brand has 99g of sugar in a 150g total pack. Zachi brand has 272g of sugar in a 400g total pack. Which product has a larger share of sugar?[cite: 19]
Concept:
1
To compare ingredient proportions accurately across different packet sizes, calculate the percentage of sugar relative to the total weight for each brand.[cite: 19]
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Hint:
1
For DEF: $\frac{99}{150} \times 100$. (Divide by 50 to get $\frac{99 \times 2}{3}$).
2
For Zachi: $\frac{272}{400} \times 100$. (Just divide 272 by 4).
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Mistakes to Avoid:
!
Comparing raw grams: Zachi has 272g of sugar compared to DEF's 99g. However, Zachi's pack is much larger. You must use percentages.
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Solution:
1. DEF Brand Sugar %:
Percentage = $\frac{99}{150} \times 100$
$= \frac{99 \times 2}{3} = 33 \times 2 = 66\%$

2. Zachi Brand Sugar %:
Percentage = $\frac{272}{400} \times 100$
$= \frac{272}{4} = 68\%$

Since $68\% > 66\%$, Zachi has a larger share of sugar.

Ans: Zachi brand has a larger share of sugar.
🎯 Marking Scheme:
• 1 Mark for DEF % (66%).
• 1 Mark for Zachi % (68%).
• 1 Mark for the correct conclusion.[cite: 19]
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3 Population Semantics Pg 16
Do the following two statements mean the same thing?
(i) The population of this state in 1991 is 165% of that in 1961.
(ii) The population of this state has increased by 65% from 1961 to 1991.[cite: 20]
Concept:
1
A value "is $X\%$ of" the base means the new value is exactly $X\%$ of the old value. A value "increased by $Y\%$" means the new value is the base ($100\%$) PLUS the increase ($Y\%$). Therefore, $100\% + Y\% = X\%$.[cite: 20]
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Hint:
1
If base $p$ increases by 65%, the new value $q = p + 65\%$ of $p$.
2
$q = 100\%$ of $p + 65\%$ of $p = 165\%$ of $p$.
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Mistakes to Avoid:
!
Confusing "of" and "by": Saying a population "increased by 165%" would mean the final population is 265% of the original. Always pay attention to the prepositions!
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Solution:
Yes, both statements mean the exact same thing.

Let population in 1961 be $p$.
Statement (i): New population $q = 165\%$ of $p = 1.65p$.
Statement (ii): New population $q = p + 65\%$ of $p$
$q = 1p + 0.65p = 1.65p$.

Ans: Yes, both mean $q = 1.65p$.
🎯 Marking Scheme:
• 1 Mark for "Yes".
• 1 Mark for the algebraic justification.[cite: 20]
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4 Retail Profit Percentage Pg 17
Kishanlal buys a sweater at a Cost Price (CP) of ₹300. He sells it at a Selling Price (SP) of ₹430. Find out the percentage profit he made on this sweater.[cite: 21]
Concept:
1
Profit = $\text{Selling Price (SP)} - \text{Cost Price (CP)}$. To find the Profit Percentage, always divide the profit by the original Cost Price, then multiply by 100.[cite: 21]
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Hint:
1
Profit = $430 - 300 = 130$.
2
Profit % = $\frac{130}{300} \times 100$. Simplify to $\frac{130}{3}$.
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Mistakes to Avoid:
!
Dividing by Selling Price: A very common error is $\frac{130}{430} \times 100$. Profit percentage must always be calculated on the base investment (Cost Price).
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Solution:
Cost Price (CP) = ₹300
Selling Price (SP) = ₹430

Profit = $\text{SP} - \text{CP} = 430 - 300 = \text{₹}130$
Profit $\%$ = $\frac{\text{Profit}}{\text{CP}} \times 100$
$= \frac{130}{300} \times 100 = \frac{130}{3}$
$= 43.33\%$

Ans: His profit percentage is 43.33%.
🎯 Marking Scheme:
• 1/2 Mark for calculating Profit (₹130).
• 1/2 Mark for setting up equation.
• 1 Mark for final % ($43.33\%$).[cite: 21]
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5 Clearing Old Stock Pg 17
Raghu's rice stock is getting old. He purchased the rice at ₹35 per kg. To clear his stock, he sells 10 kg rice for ₹300. Find out his percentage loss.[cite: 21]
Concept:
1
Loss = $\text{Cost Price (CP)} - \text{Selling Price (SP)}$. Find the total CP for 10 kg first. Then Loss % = $\frac{\text{Loss}}{\text{Total CP}} \times 100$.[cite: 21]
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Hint:
1
Total CP = $10 \times 35 = 350$.
2
Loss = $350 - 300 = 50$. Loss % = $\frac{50}{350} \times 100$.
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Mistakes to Avoid:
!
Comparing 1 kg CP to 10 kg SP: You cannot compare ₹35 to ₹300. Both values must represent the exact same quantity (10 kg).
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Solution:
Total CP for 10 kg = $10 \times 35 = \text{₹}350$
Total SP for 10 kg = ₹300

Loss = $\text{CP} - \text{SP} = 350 - 300 = \text{₹}50$
Loss $\%$ = $\frac{\text{Loss}}{\text{CP}} \times 100$
$= \frac{50}{350} \times 100 = \frac{1}{7} \times 100$
$= 14.28\%$

Ans: His loss percentage is 14.28%.
🎯 Marking Scheme:
• 1 Mark for Total CP (₹350).
• 1 Mark for Loss %.
• 1 Mark for the final answer ($14.28\%$).[cite: 21]
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6 Calculating Selling Price Pg 17
Shyamala procured a decorative vase at ₹2650. It was slightly damaged, so she decided to sell it at a loss of 18%. How much will she get by selling this piece?[cite: 21]
Concept:
1
A loss of 18% means the Selling Price is $100\% - 18\% = 82\%$ of the original Cost Price.[cite: 21]
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Hint:
1
Calculate $82\%$ of $2650$.
2
Alternatively, calculate $18\%$ of $2650$ and subtract that value from $2650$.
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Mistakes to Avoid:
!
Stopping at the loss amount: Calculating $18\%$ of $2650 = 477$ is only step 1. 477 is the *loss*, not the Selling Price. You must subtract it.
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Solution:
Method 1: Direct Percentage
Selling Price = $(100\% - 18\%)$ of CP
$= 82\%$ of $2650$
$= 0.82 \times 2650 = \text{₹}2173$

Method 2: Subtraction
Loss = $18\%$ of $2650 = \frac{18}{100} \times 2650 = 477$
SP = $\text{CP} - \text{Loss} = 2650 - 477 = \text{₹}2173$

Ans: She will sell it for ₹2173.
🎯 Marking Scheme:
• 1 Mark for calculating loss amount or finding 82%.
• 1 Mark for final SP (₹2173).[cite: 21]
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1 Comparing Scores
A student scored 18 out of 20 in Math and 21 out of 25 in Science. Which statement is true?
A. Math is better (90%)
B. Science is better (84%)
C. Both are equal
D. Cannot be compared
Concept:
1
Convert both scores to percentages to find the relative performance.
Hint:
1
Math: $\frac{18}{20} \times 100$. Science: $\frac{21}{25} \times 100$.
Mistakes to Avoid:
!
Looking at raw marks: Science has 21 marks, which is higher than 18. But the *maximum* marks are different.
Solution:
Math = $18 \times 5 = 90\%$
Science = $21 \times 4 = 84\%$
$90\% > 84\%$
Ans: Option A
2 Profit %
A toy is bought for ₹200 and sold for ₹250. What is the profit percentage?
A. 20%
B. 25%
C. 50%
D. 125%
Concept:
1
Profit % = $\frac{\text{Profit}}{\text{Cost Price}} \times 100$.
Hint:
1
Profit = $250 - 200 = 50$. Calculate $\frac{50}{200} \times 100$.
Mistakes to Avoid:
!
Dividing by SP: If you do $\frac{50}{250}$, you get 20%. Profit is always calculated on CP.
Solution:
Profit = 50
Profit % = $\frac{50}{200} \times 100 = \frac{1}{4} \times 100 = 25\%$
Ans: Option B (25%)
3 Loss %
A shirt bought for ₹400 is sold for ₹360. What is the loss percentage?
A. 10%
B. 11.11%
C. 40%
D. 90%
Concept:
1
Loss % = $\frac{\text{Loss}}{\text{Cost Price}} \times 100$.
Hint:
1
Loss = $400 - 360 = 40$. Calculate $\frac{40}{400} \times 100$.
Mistakes to Avoid:
!
Dividing by SP: If you do $\frac{40}{360} \times 100$, you get 11.11%. Loss is calculated on CP.
Solution:
Loss = 40
Loss % = $\frac{40}{400} \times 100 = \frac{1}{10} \times 100 = 10\%$
Ans: Option A (10%)
4 Finding SP from Profit
A gadget costs ₹500. The seller wants a 20% profit. What should the selling price be?
A. ₹520
B. ₹600
C. ₹100
D. ₹550
Concept:
1
SP = CP + Profit. Find $20\%$ of 500, then add it to 500. Or calculate $120\%$ of 500.
Hint:
1
$10\%$ of 500 is 50. So $20\%$ is 100.
Mistakes to Avoid:
!
Choosing the profit amount: Option C is ₹100, which is the profit, not the *selling price*. Read carefully!
Solution:
Profit = $20\%$ of $500 = 100$
SP = $500 + 100 = \text{₹}600$
Ans: Option B (₹600)
5 Semantic Wording
If a population has "increased by 40%", what percentage of the original population is the new population?
A. 40%
B. 60%
C. 140%
D. 240%
Concept:
1
Original population is 100%. "Increased by X%" means New Population = $100\% + X\%$.
Hint:
1
$100\% + 40\% = ?$
Mistakes to Avoid:
!
Answering 40%: "Is 40% of" means a reduction. "Increased by 40%" implies addition to the base 100%.
Solution:
New = $100\% + 40\% = 140\%$
Ans: Option C (140%)
1 Fruit Seller Profit
A fruit seller buys apples for ₹120 per dozen and sells them for ₹150 per dozen. Find the profit percentage.
Concept:
1
Profit = $\text{Selling Price (SP)} - \text{Cost Price (CP)}$. Profit % = $\frac{\text{Profit}}{\text{CP}} \times 100$.
Hint:
1
Profit = $150 - 120 = 30$.
2
Calculate $\frac{30}{120} \times 100$. Simplify $\frac{30}{120}$ first!
Mistakes to Avoid:
!
Dividing by SP: $\frac{30}{150} \times 100 = 20\%$. This is incorrect. Profit is relative to the investment (CP).
Solution:
CP = ₹120, SP = ₹150
Profit = $150 - 120 = 30$
Profit \% = $\frac{30}{120} \times 100$
$= \frac{1}{4} \times 100 = 25\%$

Ans: The profit percentage is 25%.
2 Calculating SP with Loss
A watch bought for ₹1500 is sold at a loss of 12%. Find the selling price.
Concept:
1
Calculate the loss amount ($12\%$ of CP) and subtract it from the CP. Alternatively, Selling Price = $(100\% - 12\%)$ of CP = $88\%$ of CP.
Hint:
1
Loss = $\frac{12}{100} \times 1500$.
2
$12 \times 15 = 180$. Subtract 180 from 1500.
Mistakes to Avoid:
!
Adding the loss: Don't accidentally do $1500 + 180 = 1680$. Loss means the SP is lower than the CP.
Solution:
Loss = $12\%$ of $1500$
$= \frac{12}{100} \times 1500 = 12 \times 15 = 180$
SP = $\text{CP} - \text{Loss} = 1500 - 180 = \text{₹}1320$

Ans: The selling price is ₹1320.
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