CBSE Class 8 Mathematics Comparing Quantities Worksheet Set 06

Question 1. Gainer loss percent is calculated on _______________ (Fill in the blanks)
Answer: Cost Price (C.P.)
In simple words: Profit or loss is always calculated based on the original cost price of the item.
Exam Tip: Always remember that percentage profit or loss is computed with respect to the Cost Price, unless specified otherwise.

Question 2. The price of a Jacket was slashed from Rs. 960 to Rs. 816. Then the rate of discount offered is
(a) 10%
(b) 15%
(c) 12.5%
(d) 5%
Answer: (b) 15%
Marked Price (M.P.) = Rs. 960
Selling Price (S.P.) = Rs. 816
Discount = Marked Price - Selling Price = 960 - 816 = Rs. 144
Discount Percentage = \(\left( \frac{\text{Discount}}{\text{Marked Price}} \right) \times 100 = \left( \frac{144}{960} \right) \times 100 = 15\%\)
In simple words: The price dropped by Rs. 144, which is 15 percent of the original marked price of Rs. 960.

Exam Tip: Discount percent is always calculated on the Marked Price (M.P.), not the Selling Price.

Question 3. 0.91 is
(a) 9.1%
(b) 0.091%
(c) 91%
(d) 0.0091%
Answer: (c) 91%
To convert a decimal to a percentage, multiply it by 100%:
\(0.91 \times 100\% = 91\%\)
In simple words: Multiply the decimal number by 100 to get its percentage equivalent.

Exam Tip: Moving the decimal point two places to the right converts any decimal into a percentage.

Question 4. The reduction in the MP is collect VAT (True / False)
Answer: False
In simple words: Reduction in the marked price is called discount, not VAT. VAT is an additional tax added to the price.

Exam Tip: Discount decreases the price, whereas taxes like VAT or GST increase the final amount to be paid.

Question 5. Net Price is the ________________ between MP and discount. (Fill in the blank)
Answer: difference
In simple words: Net price (selling price) is obtained by subtracting the discount amount from the marked price.

Exam Tip: Selling Price = Marked Price - Discount.

Question 6. Find (a) 20% of Rs. 800 (b) 16.5% of 5000m
Answer:
(a) \(20\% \text{ of Rs. } 800 = \frac{20}{100} \times 800 = \text{Rs. } 160\)
(b) \(16.5\% \text{ of } 5000\text{m} = \frac{16.5}{100} \times 5000 = \frac{165}{1000} \times 5000 = 165 \times 5 = 825\text{m}\)
In simple words: Convert the percentage into a fraction or decimal and multiply it by the given quantity.

Exam Tip: Always include the correct units (Rs. or m) in your final answer.

Question 7. Find the number x, if (a) 22% of x is 26.4 (b) 8.4% of x is 42 (c) \(\frac{1}{2}\)% of x is 50 (d) x% of 1800 is 9
Answer:
(a) \(\frac{22}{100} \times x = 26.4\)
\(x = \frac{26.4 \times 100}{22} = \frac{2640}{22} = 120\)
(b) \(\frac{8.4}{100} \times x = 42\)
\(x = \frac{42 \times 100}{8.4} = \frac{4200}{8.4} = 500\)
(c) \(\frac{0.5}{100} \times x = 50\)
\(x = \frac{50 \times 100}{0.5} = \frac{5000}{0.5} = 10000\)
(d) \(\frac{x}{100} \times 1800 = 9\)
\(18x = 9\)
\(x = \frac{9}{18} = 0.5\)
In simple words: Set up an equation with x representing the unknown number, then solve for x by isolating it.

Exam Tip: Cross-multiply carefully when dealing with decimals in fractions to avoid calculation errors.

Question 8. Balanced diet should contain 14% of proteins, 23% of fats and 63% of Carbohydrates. IF a Child needs 2600 calories in his food daily, find in calories the amount of each of these in his daily food intake.
Answer:
Total calories required = 2600 calories
Proteins = \(14\% \text{ of } 2600 = \frac{14}{100} \times 2600 = 14 \times 26 = 364 \text{ calories}\)
Fats = \(23\% \text{ of } 2600 = \frac{23}{100} \times 2600 = 23 \times 26 = 598 \text{ calories}\)
Carbohydrates = \(63\% \text{ of } 2600 = \frac{63}{100} \times 2600 = 63 \times 26 = 1638 \text{ calories}\)
In simple words: Multiply the total calorie intake by each respective percentage to find the calories from proteins, fats, and carbohydrates.

Exam Tip: You can cross-check your work by adding all calculated calories: \(364 + 598 + 1638 = 2600\).

Question 9. A garden has 2000 trees. 16% of these are mango trees, 24% lemon and the rest are orange trees. Find the number of orange trees.
Answer:
Total number of trees = 2000
Percentage of mango trees = 16%
Percentage of lemon trees = 24%
Percentage of orange trees = \(100\% - (16\% + 24\%) = 100\% - 40\% = 60\%\)
Number of orange trees = \(60\% \text{ of } 2000 = \frac{60}{100} \times 2000 = 60 \times 20 = 1200\)
In simple words: Find the remaining percentage of orange trees by subtracting mango and lemon percentages from 100%, then calculate that percentage of 2000.

Question 10. A cricketer scored a total of 62 runs in 96 balls. He hit 3 sixes, 8 fours, 2 twos and 8 singles. What is the percentage of the total runs come in -
I. Sixes
II. Fours
III. Twos
IV. Singles
Answer:
Total runs = 62
Runs from sixes = \(3 \times 6 = 18\) runs
Runs from fours = \(8 \times 4 = 32\) runs
Runs from twos = \(2 \times 2 = 4\) runs
Runs from singles = \(8 \times 1 = 8\) runs
I. Percentage from sixes = \(\left( \frac{18}{62} \right) \times 100 = \frac{900}{31} = 29.03\%\)
II. Percentage from fours = \(\left( \frac{32}{62} \right) \times 100 = \frac{1600}{31} = 51.61\%\)
III. Percentage from twos = \(\left( \frac{4}{62} \right) \times 100 = \frac{200}{31} = 6.45\%\)
IV. Percentage from singles = \(\left( \frac{8}{62} \right) \times 100 = \frac{400}{31} = 12.90\%\)
In simple words: Calculate the total runs scored through each category, divide by 62, and multiply by 100 to convert to a percentage.
Exam Tip: Verify that the sum of all calculated runs equals 62 (\(18 + 32 + 4 + 8 = 62\)) before finding percentages.

Question 11. Aman's income is 20% less than that of Anil. What percent is Anil's income more than that of Aman.
Answer:
Let Anil's income = Rs. 100
Aman's income is 20% less than Anil's income:
Aman's income = \(100 - 20\% \text{ of } 100 = \text{Rs. } 80\)
Difference between their incomes = \(100 - 80 = \text{Rs. } 20\)
Anil's income is more than Aman's income by Rs. 20.
Percentage by which Anil's income is more than Aman's = \(\left( \frac{\text{Difference}}{\text{Aman's Income}} \right) \times 100 = \left( \frac{20}{80} \right) \times 100 = 25\%\)
In simple words: Although Aman earns 20% less relative to Anil, Anil earns 25% more relative to Aman's lower base salary.

Exam Tip: A common mistake is assuming the answer is 20%. Always divide by the base of the person being compared against (Aman in this case).

Question 12. 75% of the total number of students, didn't go for picnic. Those who went for the picnic were 750. Find the total number of students in the school.
Answer:
Percentage of students who didn't go for picnic = 75%
Percentage of students who went for picnic = \(100\% - 75\% = 25\%\)
Let the total number of students be x.
\(25\% \text{ of } x = 750\)
\(\frac{25}{100} \times x = 750\)
\(x = \frac{750 \times 100}{25} = 30 \times 100 = 3000\)
In simple words: If 75% stayed home, 25% went on the picnic. Since 25% represents 750 students, multiplying by 4 gives the total student population of 3000.

Exam Tip: First find the percentage corresponding to the given actual number before setting up the equation.

Question 13. In the new Budget, the Price of Petrol rose by 10%. By how much percent must one reduce the consumption so that the expenditure does not increase.
Answer:
Let the original price of 1 litre of petrol = Rs. 100 and initial consumption = 1 litre.
Initial expenditure = \(100 \times 1 = \text{Rs. } 100\)
New price after a 10% increase = \(\text{Rs. } 110\)
To keep the expenditure constant at Rs. 100, the new consumption for Rs. 100 becomes:
New consumption = \(\frac{100}{110} = \frac{10}{11} \text{ litres}\)
Reduction in consumption = \(1 - \frac{10}{11} = \frac{1}{11} \text{ litres}\)
Percentage reduction in consumption = \(\left( \frac{\frac{1}{11}}{1} \right) \times 100 = \frac{100}{11}\% = 9.09\%\)
In simple words: To offset a 10% price increase without spending more, consumption must be reduced by approximately 9.09%.

Exam Tip: Use the formula \(\left( \frac{r}{100 + r} \right) \times 100\%\) where r is the percentage increase in price for a quick shortcut.

Question 14. The winning percentage of Indian Cricket Team is 60% of the total number of matches which were played by it during the year. IF the team lost 12 matches in all and no match was drawn, find the total number of matches played by the team during the year.
Answer:
Winning percentage = 60%
Since no matches were drawn, the losing percentage = \(100\% - 60\% = 40\%\)
Let the total number of matches played be x.
Given that the team lost 12 matches:
\(40\% \text{ of } x = 12\)
\(\frac{40}{100} \times x = 12\)
\(x = \frac{12 \times 100}{40} = \frac{1200}{40} = 30\)
In simple words: If the team won 60% and there were no draws, they lost 40%. Since 40% equals 12 matches, the total number of matches played is 30.

Exam Tip: Ensure you account for the "no matches drawn" condition, which implies total matches = wins + losses.

Question 15. Sony spends 25% of her salary on food and donates 5% of her salary in a charitable trust. In a particular month she spent Rs. 2,310 on these 2 items. What is her total salary for this month?
Answer:
Percentage spent on food = 25%
Percentage donated = 5%
Total percentage spent on these two items = \(25\% + 5\% = 30\%\)
Let her total monthly salary be x.
\(30\% \text{ of } x = 2310\)
\(\frac{30}{100} \times x = 2310\)
\(x = \frac{2310 \times 100}{30} = \frac{231000}{30} = \text{Rs. } 7700\)
In simple words: Sony spends a combined 30% of her salary on food and charity. Since this equals Rs. 2,310, her total salary is Rs. 7,700.

Exam Tip: Add the percentages together first before setting up the equation with the total amount spent.

Question 16. By selling a pen for Rs. 60. Shyam gains 25%. Find the C.P. of the pen.
Answer:
Selling Price (S.P.) = Rs. 60
Gain percentage = 25%
Cost Price (C.P.) = \(\left( \frac{100}{100 + \text{Gain}\%} \right) \times \text{S.P.}\)
\(\text{C.P.} = \left( \frac{100}{100 + 25} \right) \times 60 = \frac{100}{125} \times 60 = \frac{4}{5} \times 60 = 4 \times 12 = \text{Rs. } 48\)
In simple words: Working backward from the selling price and profit percentage, the original cost price of the pen was Rs. 48.

Exam Tip: Memorize the formula \(\text{C.P.} = \frac{100}{100 + \text{Gain}\%} \times \text{S.P.}\) for direct calculations.

Question 17. By selling 8 dozen of pencils, a shopkeeper gains the selling price of one dozen pencils. Find his gain percentage.
Answer:
Let the selling price of 1 dozen pencils = Rs. 1
Selling Price (S.P.) of 8 dozen pencils = Rs. 8
Gain = Selling price of 1 dozen pencils = Rs. 1
Cost Price (C.P.) of 8 dozen pencils = \(\text{S.P.} - \text{Gain} = 8 - 1 = \text{Rs. } 7\)
Gain percentage = \(\left( \frac{\text{Gain}}{\text{C.P.}} \right) \times 100 = \left( \frac{1}{7} \right) \times 100 = \frac{100}{7}\% = 14.28\%\)
In simple words: The shopkeeper makes a profit equal to 1 dozen out of 8 dozen sold, giving a gain percentage of \(14.28\%\).

Exam Tip: Profit percentage is always calculated on Cost Price, not Selling Price. Ensure you subtract the profit from total S.P. to find C.P.

Question 18. Harish bought a cycle for Rs. 480 and sold it to Satish at a profit of 6%. Satish sold the same to Girish at a profit of 10%. For how much did Girish get it?
Answer:
Cost Price for Harish = Rs. 480
Harish sells to Satish at a profit of 6%:
Selling Price for Harish (Cost Price for Satish) = \(480 + 6\% \text{ of } 480 = 480 \times \frac{106}{100} = \text{Rs. } 508.80\)
Satish sells to Girish at a profit of 10%:
Selling Price for Satish (Cost Price for Girish) = \(508.80 + 10\% \text{ of } 508.80 = 508.80 \times \frac{110}{100} = 508.80 \times 1.10 = \text{Rs. } 559.68\)
In simple words: Calculate successive profits by applying each percentage increase sequentially to the updated price.

Exam Tip: You can combine successive percentage increases directly: \(480 \times 1.06 \times 1.10 = 559.68\).

Question 19. Soniya buys 2 watches for Rs. 1200 each. She sells one at a profit of 10% and other at a loss of 5%. Find her gain and loss percentage.
Answer:
Cost Price of 1st watch = Rs. 1200, Profit = 10%
Selling Price of 1st watch = \(1200 \times \frac{110}{100} = \text{Rs. } 1320\)
Cost Price of 2nd watch = Rs. 1200, Loss = 5%
Selling Price of 2nd watch = \(1200 \times \frac{95}{100} = \text{Rs. } 1140\)
Total Cost Price (C.P.) = \(1200 + 1200 = \text{Rs. } 2400\)
Total Selling Price (S.P.) = \(1320 + 1140 = \text{Rs. } 2460\)
Since Total S.P. > Total C.P., there is an overall profit.
Total Profit = \(2460 - 2400 = \text{Rs. } 60\)
Overall Profit Percentage = \(\left( \frac{\text{Total Profit}}{\text{Total C.P.}} \right) \times 100 = \left( \frac{60}{2400} \right) \times 100 = \frac{60}{24} = 2.5\%\)
In simple words: Combine the total cost and total selling prices of both watches to find an overall net profit of 2.5%.

Exam Tip: When individual items have the same cost price, the net profit/loss percentage is simply the average of the individual profit/loss percentages: \(\frac{10\% - 5\%}{2} = 2.5\%\).

Question 20. Suresh buys a V.C.D. player for Rs. 6,500. He sells it to Chaman at a profit of 8%. Chaman sells it to Mukesh at a profit of 10%. How much Mukesh pay for the V.C.D. player?
Answer:
Cost Price for Suresh = Rs. 6500
Suresh sells to Chaman at 8% profit:
Selling Price for Suresh (Cost Price for Chaman) = \(6500 \times \frac{108}{100} = 65 \times 108 = \text{Rs. } 7020\)
Chaman sells to Mukesh at 10% profit:
Selling Price for Chaman (Cost Price for Mukesh) = \(7020 \times \frac{110}{100} = 702 \times 11 = \text{Rs. } 7722\)
In simple words: Mukesh pays Rs. 7,722 after accounting for successive profits by Suresh and Chaman.

Exam Tip: Multiply the base price directly by the multiplier factors: \(6500 \times 1.08 \times 1.10 = 7722\).

Question 21. The marked price of a ceiling fan is Rs. 720. During off season, it is sold for Rs. 684. Find the discount percent.
Answer:
Marked Price (M.P.) = Rs. 720
Selling Price (S.P.) = Rs. 684
Discount = \(\text{M.P.} - \text{S.P.} = 720 - 684 = \text{Rs. } 36\)
Discount Percentage = \(\left( \frac{\text{Discount}}{\text{M.P.}} \right) \times 100 = \left( \frac{36}{720} \right) \times 100 = \frac{1}{20} \times 100 = 5\%\)
In simple words: The discount is Rs. 36, which is 5 percent of the Rs. 720 marked price.

Exam Tip: Always divide the discount by the Marked Price, never the Selling Price, when calculating discount percentage.

Question 22. List price of a scooter is Rs. 3,500. It is available at a discount of 8%. Find the S.P. of the scooter.
Answer:
Marked Price (List Price) = Rs. 3500
Discount = 8%
Selling Price (S.P.) = \(\text{List Price} \times \left( \frac{100 - \text{Discount}\%}{100} \right)\)
\(\text{S.P.} = 3500 \times \left( \frac{100 - 8}{100} \right) = 3500 \times \frac{92}{100} = 35 \times 92 = \text{Rs. } 3220\)
In simple words: Subtracting an 8% discount from the list price gives a selling price of Rs. 3,220.

Exam Tip: You can also find 8% of 3500 (which is Rs. 280) and subtract it from 3500 to get the same result.

Question 23. Find the marked price of an almirah which is sold at Rs. 5,225 after allowing a discount of 5%.
Answer:
Selling Price (S.P.) = Rs. 5225
Discount percentage = 5%
Marked Price (M.P.) = \(\left( \frac{100}{100 - \text{Discount}\%} \right) \times \text{S.P.}\)
\(\text{M.P.} = \left( \frac{100}{100 - 5} \right) \times 5225 = \frac{100}{95} \times 5225 = \frac{20}{19} \times 5225 = 20 \times 275 = \text{Rs. } 5500\)
In simple words: Working backward from the selling price and discount rate, the original marked price of the almirah was Rs. 5,500.

Exam Tip: Use the formula \(\text{M.P.} = \frac{100}{100 - \text{Discount}\%} \times \text{S.P.}\) when finding marked price from selling price.

Question 24. A poor lady was shivering in cold. She went to a shop to purchase a shawl. But she had only Rs. 680 with her. The shopkeeper noticed the condition of the poor lady and sold the shawl for Rs. 680 after allowing a discount of 40% on the Market Price.
(i) Find the marked price of the shawl.
(ii) What quality is shown by the shopkeeper.
Answer:
(i) Selling Price (S.P.) = Rs. 680
Discount percentage = 40%
Marked Price (M.P.) = \(\left( \frac{100}{100 - \text{Discount}\%} \right) \times \text{S.P.}\)
\(\text{M.P.} = \left( \frac{100}{100 - 40} \right) \times 680 = \frac{100}{60} \times 680 = \frac{5}{3} \times 680 = \frac{3400}{3} = \text{Rs. } 1133.33\)
(ii) The shopkeeper displays empathy, kindness, compassion, and helpfulness towards the needy.
In simple words: (i) The original marked price was Rs. 1,133.33. (ii) The shopkeeper showed a kind and generous heart by helping someone in need.

Exam Tip: Value-based questions in mathematics require both an accurate numerical calculation and a thoughtful moral observation.

Question 25. Mr. Narang purchased a camera for Rs. 2,365 including 10% tax. Find the M.P. of the camera.
Answer:
Price including tax = Rs. 2365
Tax rate = 10%
Let the Marked Price (or original price before tax) be x.
\(x + 10\% \text{ of } x = 2365\)
\(1.10x = 2365\)
\(x = \frac{2365}{1.10} = \frac{236500}{110} = \text{Rs. } 2150\)
In simple words: Removing the 10% tax from the final purchase price reveals that the original marked price of the camera was Rs. 2,150.

Exam Tip: Tax is always added to the base price, so price with tax = \(\text{Base Price} \times (1 + \frac{\text{Tax}\%}{100})\).

Question 26. The list price of a coloured T.V. is Rs. 17,650. If the sales tax is 8%. Find the sales price.
Answer:
List Price = Rs. 17650
Sales tax rate = 8%
Sales tax amount = \(8\% \text{ of } 17650 = \frac{8}{100} \times 17650 = \text{Rs. } 1412\)
Sales Price (Total amount to be paid) = List Price + Sales Tax
\(\text{Sales Price} = 17650 + 1412 = \text{Rs. } 19062\)
In simple words: Add an 8% sales tax of Rs. 1,412 to the list price to get the total selling price of Rs. 19,062.

Question 27. Naresh paid Rs. 20 on sales tax on a pair of shoes worth Rs. 250. Find the rate of sales tax.
Answer:
Price of shoes (Base value) = Rs. 250
Sales tax paid = Rs. 20
Rate of sales tax = \(\left( \frac{\text{Sales Tax}}{\text{Base Price}} \right) \times 100 = \left( \frac{20}{250} \right) \times 100 = \frac{2}{25} \times 100 = 2 \times 4 = 8\%\)
In simple words: Dividing the sales tax amount by the price of the shoes gives a tax rate of 8%.

Exam Tip: Sales tax percentage is calculated relative to the original item price, exactly like profit percentage.