Comparing Quantities - Class 7 - Mathematics
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Examples - Comparing Quantities | NCERT | Mathematics | Class 7
Write $\frac{1}{3}$ as per cent.
To write $\frac{1}{3}$ as a percent, multiply by 100%:
$$\frac{1}{3} \times 100% = \frac{100}{3}% = 33.\overline{3}%$$
Therefore, $\frac{1}{3}$ expressed as a percent is $33.\overline{3}%$.
Out of 25 children in a class, 15 are girls. What is the percentage of girls?
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Sign up nowConvert $\frac{5}{4}$ to per cent
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Sign up nowConvert the given decimals to per cents:
(a) 0.75
(b) 0.09
(c) 0.2
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Sign up nowA survey of 40 children showed that $25 \%$ liked playing football. How many children liked playing football?
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Sign up nowRahul bought a sweater and saved $₹ 200$ when a discount of $25 \%$ was given. What was the price of the sweater before the discount?
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Sign up nowReena's mother said, to make idlis, you must take two parts rice and one part urad dal. What percentage of such a mixture would be rice and what percentage would be urad dal?
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Sign up nowIf ₹ 250 is to be divided amongst Ravi, Raju and Roy, so that Ravi gets two parts, Raju three parts and Roy five parts. How much money will each get? What will it be in percentages?
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Sign up nowA school team won 6 games this year against 4 games won last year. What is the per cent increase?
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Sign up nowThe number of illiterate persons in a country decreased from 150 lakhs to 100 lakhs in 10 years. What is the percentage of decrease?
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Sign up nowSelling price of a toy car is ₹ 540 . If the profit made by shopkeeper is $20 \%$, what is the cost price of this toy?
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Sign up nowAnita takes a loan of ₹ 5,000 at $15 \%$ per year as rate of interest. Find the interest she has to pay at the end of one year.
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Sign up nowIf Manohar pays an interest of ₹ 750 for 2 years on a sum of $₹ 4,500$, find the rate of interest.
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Sign up nowExercise 7.1 - Comparing Quantities | NCERT | Mathematics | Class 7
Convert the given fractional numbers to per cents.
(a) $\frac{1}{8}$
(b) $\frac{5}{4}$
(c) $\frac{3}{40}$
(d) $\frac{2}{7}$
Here are the conversions of the given fractional numbers to percents:
(a) $\frac{1}{8}$ is equivalent to $12.5%$
(b) $\frac{5}{4}$ is equivalent to $125%$
(c) $\frac{3}{40}$ is equivalent to $7.5%$
(d) $\frac{2}{7}$ is equivalent to $28.57%$
Convert the given decimal fractions to per cents.
(a) 0.65
(b) 2.1
(c) 0.02
(d) 12.35
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Sign up nowEstimate what part of the figures is coloured and hence find the per cent which is coloured.
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Sign up nowFind:
(a) $15 \%$ of 250
(b) $1 \%$ of 1 hour
(c) $20 \%$ of ₹ 2500
(d) $75 \%$ of $1 \mathrm{~kg}$
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Sign up nowFind the whole quantity if
(a) $5 \%$ of it is 600 .
(b) $12 \%$ of it is ₹ 1080 .
(c) $40 \%$ of it is $500 \mathrm{~km}$.
(d) $70 \%$ of it is 14 minutes.
(e) $8 \%$ of it is 40 litres.
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Sign up nowConvert given per cents to decimal fractions and also to fractions in simplest forms:
(a) $25 \%$
(b) $150 \%$
(c) $20 \%$
(d) $5 \%$
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Sign up nowIn a city, $30 \%$ are females, $40 \%$ are males and remaining are children. What per cent are children?
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Sign up nowOut of 15,000 voters in a constituency, $60 \%$ voted. Find the percentage of voters who did not vote. Can you now find how many actually did not vote?
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Sign up nowMeeta saves ₹ 4000$ from her salary. If this is $10 \%$ of her salary. What is her salary?
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Sign up nowA local cricket team played 20 matches in one season. It won $25 \%$ of them. How many matches did they win?
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Sign up nowExercise 7.2 - Comparing Quantities | NCERT | Mathematics | Class 7
Tell what is the profit or loss in the following transactions. Also find profit per cent or loss per cent in each case.
(a) Gardening shears bought for ₹ 250 and sold for ₹ 325 .
(b) A refrigerater bought for ₹ 12,000 and sold at ₹ 13,500 .
(c) A cupboard bought for ₹ 2,500 and sold at ₹ 3,000.
(d) A skirt bought for ₹ 250 and sold at ₹ 150 .
Let's calculate the profit or loss for each transaction, along with its percentage.
Gardening Shears
Bought for ₹250 and sold for ₹325.
Profit = Selling Price - Cost Price = ₹325 - ₹250 = ₹75.
Profit Percent = (Profit / Cost Price) * 100 = (₹75 / ₹250) * 100 = 30%.
Refrigerator
Bought for ₹12,000 and sold at ₹13,500.
Profit = Selling Price - Cost Price = ₹13,500 - ₹12,000 = ₹1,500.
Profit Percent = (Profit / Cost Price) * 100 = (₹1,500 / ₹12,000) * 100 = 12.5%.
Cupboard
Bought for ₹2,500 and sold at ₹3,000.
Profit = Selling Price - Cost Price = ₹3,000 - ₹2,500 = ₹500.
Profit Percent = (Profit / Cost Price) * 100 = (₹500 / ₹2,500) * 100 = 20%.
Skirt
Bought for ₹250 and sold at ₹150.
Loss = Cost Price - Selling Price = ₹250 - ₹150 = ₹100.
Loss Percent = (Loss / Cost Price) * 100 = (₹100 / ₹250) * 100 = 40%.
For each case, we calculated the difference between the selling price and the cost price to determine if there is a profit (selling price is more than cost price) or a loss (selling price is less than cost price). The percentage was then calculated by dividing the profit or loss by the cost price and multiplying by 100.
Convert each part of the ratio to percentage:
(a) $3: 1$
(b) $2: 3: 5$
(c) $1: 4$
(d) $1: 2: 5$
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Sign up nowThe population of a city decreased from 25,000 to 24,500 . Find the percentage decrease.
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Sign up nowArun bought a car for ₹ $3,50,000$. The next year, the price went upto ₹ 3,70,000$. What was the Percentage of price increase?
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Sign up nowI buy a T.V. for ₹ 10,000 and sell it at a profit of $20 \%$. How much money do I get for it?
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Sign up nowJuhi sells a washing machine for ₹ 13,500 . She loses $20 \%$ in the bargain. What was the price at which she bought it?
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Sign up now(i) Chalk contains calcium, carbon and oxygen in the ratio 10:3:12. Find the percentage of carbon in chalk.
(ii) If in a stick of chalk, carbon is $3 \mathrm{~g}$, what is the weight of the chalk stick?
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Sign up nowAmina buys a book for ₹ 275 and sells it at a loss of $15 \%$. How much does she sell it for?
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Sign up nowFind the amount to be paid at the end of 3 years in each case:
(a) Principal $= ₹ 1,200$ at $12 \%$ p.a.
(b) Principal $= ₹ 7,500$ at $5 \%$ p.a.
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Sign up nowWhat rate gives ₹ 280 as interest on a sum of ₹ 56,000 in 2 years?
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Sign up nowIf Meena gives an interest of ₹ 45 for one year at $9 \%$ rate p.a.. What is the sum she has borrowed?
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Sign up nowExtra Questions - Comparing Quantities | NCERT | Mathematics | Class 7
A 10-inch long candle lasts for 45 minutes. How long will another candle of the same material and the same thickness but 4 inches longer than the previous one last?
A) 60 minutes
B) 71 minutes
C) 63 minutes
D) 65 minutes
The correct answer is Option C: 63 minutes.
We can analyze the problem using direct proportion since the burn rate is constant per inch of the candle. The rate of burning depends solely on the length of the candle, and both candles have the same thickness and are made from the same material.
Let's calculate the time $ t $ it will take for the $ 14 $-inch candle to burn. Given:
Original candle length: $ 10 $ inches
Original candle lifespan: $ 45 $ minutes
New candle length: $ 14 $ inches (original $ 10 $ inches plus $ 4 $ inches)
Since the problem involves direct variation, the time to burn the whole candle is proportional to its length. Thus, $$ t = \frac{45 \times 14}{10} $$ This simplifies to: $$ t = \frac{45 \times 14}{10} = 63 \text{ minutes} $$ Thus, the $ 14 $-inch candle will last for 63 minutes.
Shubendhu buys an old scooter for Rs. 4700 and spends Rs. 800 on its repairs. If he sells the scooter for Rs. 5800, his gain (in percentage) is:
(A) $65/12$ (B) $71/11$ (C) $60/11$ (D) $77/12$
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Sign up now'x exceeds y by 7' can be expressed as...?
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