COMPARING QUANTITIES
Main Concepts and Results:
• To compare two quantities, their units must be the same.
• Two ratios can be compared by converting them into like fractions. If the two fractions are
equal, we say that the two given ratios are equivalent.
• If two ratios are equivalent (or equal), then the involved four quantities are said to be in
proportion.
• One of the ways of comparing quantities is percentage. Per cent is derived from Latin
word ‘per centum’ meaning ‘per hundred’.
• Percent is represented by the symbol % and means hundredth too.
• Fractions can be converted into percentages and vice-versa.
• Decimals can also be converted into percentages and vice-versa.
• The buying price of any item is known as its cost price. It is written in short as CP.
• The price at which an item is sold, is known as its selling price or in short SP.
• If CP < SP, then a profit is made and Profit = SP – CP.
• If CP = SP, there is no profit or loss.
• If CP > SP, then a loss is made and Loss = CP – SP.
• Profit per cent =
• Loss per cent =
X 100
X 100
• ‘Principal’ P, means the borrowed money.
• The extra money paid by borrower for using borrowed money for given time is called
‘Interest’ I.
• The period for which the money is borrowed is called ‘Time Period’ T.
• To determine Interest to be paid, we have ‘Rate of Interest’.
• Rate of Interest is generally given in per cent per year.
• On a principal of Rs. P at R % rate of interest per year, the interest (simple) I paid for T
years is given by I =
×
×
• The total money paid alongwith interest or principal P is called amount (A). Thus A = P + I.
Exercise:
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9)
To compare two quantities, the units must be the same. State whether true or false?
Find the ratio of 3 km to 300 m.
Are the ratios 1:2 and 2:3 equivalent?
Following is the performance of a cricket team in the matches it played:
In which year was the record better? How can you say so?
A map is given with a scale of 2 cm = 1000 km. What is the actual distance between
the two places in kms, if the distance in the map is 2.5 cm?
6 bowls cost Rs 90. What would be the cost of 10 such bowls?
The car that I own can go 150 km with 25 litres of petrol. How far can it go with 30
litres of petrol?
Find the ratio of:
(a) Rs 5 to 50 paise
(b) 15 kg to 210 g
(c) 9 m to 27 cm
(d) 30 days to 36 hour
In a computer lab, there are 3 computers for every 6 students. How many computers
will be needed for 24 students?
10) Population of Rajasthan = 570 lakhs and population of UP = 1660 lakhs. Area of
Rajasthan = 3 lakh km2 and area of UP = 2 lakh km2.
(i) How many people are there per km2 in both these States?
(ii) Which State is less populated?
11) What do you understand by the term “percentage”?
12) Anita said that she has done better as she got 320 marks out of 400 whereas Rita got
only 300 marks out of 360. Do you agree with her? Who do you think has done
better?
13) Nina got 850 marks out of 1020 in her final exam. Then what is her percentage of
marks?
14) Nina got 850 marks out of 1000 in her final exam. Then what is her percentage of
marks?
15) Find the Percentage of children of different heights for the following data.
16) A shop has the following number of shoe pairs of different sizes.
Size 2 : 20
Size 3 : 30
Size 4 : 28
Size 5 : 14
Size 6 : 8
Write this information in tabular form as done earlier and find the Percentage of
each shoe size available in the shop.
17) Mala has a collection of bangles. She has 20 gold bangles and 10 silver bangles. What
is the percentage of bangles of each type? Can you put it in the tabular form?
18) Write
as per cent.
19) Out of 25 children in a class, 15 are girls. What is the percentage of girls?
20) Convert
to per cent.
21) Convert the given decimals to per cents:
(a) 0.75
(b) 0.09
(c) 0.2
22) Convert the following to per cents:
(a) 12/ 16
(b) 3.5
(c)49/50
(d)2/ 2
(e) 0.05
23) (i) Out of 32 students, 8 are absent. What per cent of the students are absent?
(ii) There are 25 radios, 16 of them are out of order. What per cent of radios are out
of order?
(iii) A shop has 500 parts, out of which 5 are defective. What per cent are defective?
(iv) There are 120 voters , 90 of them voted yes. What per cent voted yes?
24) If 65% of students in a class have a bicycle, what per cent of the student do not
have bicycles?
25) We have a basket full of apples, oranges and mangoes. If 50% are apples, 30% are
oranges, then what per cent are mangoes?
26) What per cent of the below figure is shaded?
27) What per cent of these figures are shaded?
28) A survey of 40 children showed that 25% liked playing football. How many children
liked playing football?
29) Find:
(a) 50% of 164
(b) 75% of 12
(c) 12 % of 64
30) 8% children of a class of 25 like getting wet in the rain. How many children like
getting wet in the rain.
31) Rahul bought a sweater and saved Rs 20 when a discount of 25% was given. What
was the price of the sweater before the discount?
32) 9 is 25% of what number?
33) 75% of what number is 15?
34) Convert the given fractional numbers to per cents
35) Convert the given decimal fractions to per cents.
(a) 0.65
(b) 2.1
(c) 0.02
(d) 12.35
36) Estimate what part of the figures is coloured and hence find the per cent which is
coloured.
37) Find:
a) 15% of 250
(b) 1% of 1 hour
(c) 20% of ` 2500
(d) 75% of 1 kg
38) Find the whole quantity if
(a) 5% of it is 600.
(b) 12% of it is Rs 1080.
(c) 40% of it is 500 km.
(d) 70% of it is 14 minutes.
39) Convert given per cents to decimal fractions and also to fractions in simplest forms:
(a) 25%
(b) 150%
(c) 20%
(d) 5%
40) In a city, 30% are females, 40% are males and remaining are children. What per cent
are children?
41) Out 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?
42) Meeta saves Rs 400 from her salary. If this is 10% of her salary. What is her salary?
43) A local cricket team played 20 matches in one season. It won 25% of them. How
many matches did they win?
44) Reena’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?
45) If Rs 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?
46) Divide 15 sweets between Manu and Sonu so that they get 20 % and 80 % of them
respectively.
47) If angles of a triangle are in the ratio 2 : 3 : 4. Find the value of each angle.
48) A school team won 6 games this year against 4 games won last year. What is the per
cent increase?
49) The number of illiterate persons in a country decreased from 150 lakhs to 100 lakhs
in 10 years. What is the percentage of decrease?
50) Find Percentage of increase or decrease:
– Price of shirt decreased from Rs 80 to Rs 60.
– Marks in a test increased from 20 to 30.
51) Define the terms : (i) Cost price (ii) Selling price
(iii) Profit
(iv) Loss
52) The cost of a flower vase is Rs 120. If the shopkeeper sells it at a loss of 10%, find the
price at which it is sold.
53) Selling price of a toy car is Rs 540. If the profit made by shopkeeper is 20%, what is
the cost price of this toy?
54) A shopkeeper bought a chair for Rs 375 and sold it for Rs 400. Find the gain
Percentage.
55) Cost of an item is Rs 50. It was sold with a profit of 12%. Find the selling price.
56) An article was sold for Rs 250 with a profit of 5%. What was its cost price?
57) An item was sold for RS 540 at a loss of 5%. What was its cost price?
58) Define the terms : (i) Principal
(ii) Interest
(iii) Amount
59) Anita takes a loan of Rs 5,000 at 15% per year as rate of interest. Find the interest
she has to pay at the end of one year.
60) What do you mean by the term “simple interest”?
61) Rs10,000 is invested at 5% interest rate p.a. Find the interest at the end of one year.
62) Rs3,500 is given at 7% p.a. rate of interest. Find the interest which will be received at
the end of two years.
63) Rs 6,050 is borrowed at 6.5% rate of interest p.a.. Find the interest and the amount
to be paid at the end of 3 years.
64) Rs 7,000 is borrowed at 3.5% rate of interest p.a. borrowed for 2 years. Find the
amount to be paid at the end of the second year.
65) If Manohar pays an interest of Rs750 for 2 years on a sum of Rs 4,500, find the rate
of interest.
66) You have Rs 2,400 in your account and the interest rate is 5%. After how many years
would you earn Rs 240 as interest.
67) On a certain sum the interest paid after 3 years is Rs 450 at 5% rate of interest per
annum. Find the sum.
68) 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 Rs 250 and sold for Rs325.
(b) A refrigerator bought for Rs 12,000 and sold at Rs 13,500.
(c) A cupboard bought for Rs 2,500 and sold at Rs 3,000.
(d) A skirt bought for Rs 250 and sold at Rs 150.
69) Convert each part of the ratio to percentage:
(a) 3:1
(b) 2:3:5
(c) 1:4
(d) 1:2:5
70) The population of a city decreased from 25,000 to 24,500. Find the percentage
decrease.
71) Arun bought a car for Rs 3,50,000. The next year, the price went up to Rs 3,70,000.
What was the Percentage of price increase?
72) I buy a T.V. for Rs 10,000 and sell it at a profit of 20%. How much money do I get for
it?
73) Juhi sells a washing machine for Rs 13,500. She loses 20% in the bargain. What was
the price at which she bought it?
74) (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 3g, what is the weight of the chalk stick?
75) Amina buys a book for Rs 275 and sells it at a loss of 15%. How much does she sell it
for?
76) Find the amount to be paid at the end of 3 years in each case:
(a) Principal = RS 1,200 at 12% p.a.
(b) Principal = Rs7,500 at 5% p.a.
77) What rate gives Rs 280 as interest on a sum of Rs 56,000 in 2 years?
78) If Meena gives an interest of Rs 45 for one year at 9% rate p.a.. What is the sum she
has borrowed?
Multiple Choice Questions:
1) The ratio of the heights 1.50 m and 75 cm of two persons can be written as
(a) 1 : 50
(b) 1 : 5
(c) 2 : 1
(d) 1 : 2
2) Out of 50 children in a class, 20 are boys. Then the percentage of girls is
(a) 60
(b) 30
(c) 50
(d) 66
3) The interest on Rs 5000 at the rate of 15% per annum for one month is
4) The interest on Rs 5000 at the rate of 15% per annum for one month is
5) 20% of 700 m is
(a) 560 m
(b) 70 m
(c) 210 m
(d) 140 m
6) Gayatri’s income is Rs 1,60,000 per year. She pays 15% of this as house rent
and 10% of the remainder on her child’s education. The money left with her
is:
7) The ratio of Fatima’s income to her savings is 4 : 1. The percentage of money
saved by her is :
(a) 20%
(b) 25%
(c) 40%
(d) 80%
8) 0.07 is equal to
(a) 70%
(b) 7%
(c) 0.7%
(d) 0.07%
9) In a scout camp, 40% of the scouts were from Gujarat State and 20% of these
were from Ahmedabad. The percentage of scouts in the camp from
Ahmedabad is:
(a) 25
(b) 32.5
(c) 8
(d) 50
10) What percent of Rs 4500 is Rs 9000?
(a) 200
(b)1/ 2
(c) 2
(d) 50
11) 5.2 is equal to
(a) 52%
(b) 5.2%
(c) 520%
(d) 0.52%
12) The ratio 3 : 8 is equal to
(a) 3.75%
13) 225% is equal to
(a) 9 : 4
(b) 37.5%
(c) 0.375%
(d) 267%
(b) 4 : 9
(c) 3 : 2
(d) 2 : 3
14) A bicycle is purchased for Rs 1800 and is sold at a profit of 12%.Its selling
price is
15) A cricket bat was purchased for Rs 800 and was sold for Rs 1600. Then
profit earned is
(a) 100%
(b) 64%
(c) 50%
(d) 60%
16) A farmer bought a buffalo for Rs 44000 and a cow for Rs 18000. He sold the
buffalo at a loss of 5% but made a profit of 10% on the cow. The net result of
the transaction is
17) If Mohan’s income is 25% more than Raman’s income, then Raman’s income
is less than Mohan’s income by
(a) 25%
(b) 80%
(c) 20%
(d) 75%
18) The interest on Rs 30000 for 3 years at the rate of 15% per annum is
19) Amount received on Rs 3000 for 2 years at the rate of 11% per annum is
(a)Rs 2340
(b)Rs 3660
(c)Rs4320
(d)Rs 3330
20) Interest on Rs 12000 for 1 month at the rate of 10 % per annum is
a) Rs 1200
(b)Rs 600
(c)Rs 100
(d)Rs 12100
21) If 90% of x is 315 km, then the value of x is
(a) 325 km
(b) 350 km
(c) 405 km
(d) 340 km
22) On selling an article for Rs 329, a dealer lost 6%. The cost price of the article
is
23) Rajni and Mohini deposited Rs 3000 and Rs 4000 in a company at the rate of
10% per annum for 3 years and 2 years respectively. The difference of the
24)
amounts received by them will be
(a)Rs 100
(b)Rs 1000
(c)Rs 900
%
(a) 1.1%
%
×
%
is equal to
(b) 0.1%
(c) 0.01%
(d)Rs 1100
(d) 1%
25) The sum which will earn a simple interest of Rs 126 in 2 years at 14% per
annum is
26) The per cent that represents the un shaded region in the figure.
(a) 75%
(b) 50%
(c) 40%
(d) 60
27) The per cent that represents the shaded region in the figure is
a) 36%
(b) 64%
(c) 27%
Fill in the blanks to make the statements true.
(d) 48%
28) 2 : 3 = ________ %
29) 18 % = _______ : _______
30) 30% of Rs 360 = ______
31) 120 % of 50 km = ________.
32) 2.5 = ________%
33) = _______%.
34) A _______ with its denominator 100 is called a per cent.
35) 15 kg is _______ % of 50 kg.
36) Weight of Nikhil increased from 60 kg to 66 kg. Then, the increase in weight is
_______ %.
37) In a class of 50 students, 8 % were absent on one day. The number of
students present on that day was ________.
38) Savitri obtained 440 marks out of 500 in an examination. She secured
_______ % marks in the examination
39) Out of a total deposit of Rs 1500 in her bank account, Abida withdrew 40% of
the deposit. Now the balance in her account is ______.
40) ________ is 50% more than 60.
41) John sells a bat for Rs 75 and suffers a loss of Rs 8. The cost price of the bat is
________.
42) If the price of sugar is decreased by 20%, then the new price of 3kg sugar
originally costing Rs 120 will be_____.
43) Mohini bought a cow for Rs 9000 and sold it at a loss of Rs 900. The selling
price of the cow is ________.
44) Devangi buys a chair for Rs 700 and sells it for Rs 750. She earns a profit of
________ % in the transaction.
45) Sonal bought a bed sheet for Rs 400 and sold it for Rs 440. Her ________% is
________.
46) Nasim bought a pen for Rs 60 and sold it for Rs 54. His ________% is
________.
47) Aahuti purchased a house for Rs 50,59,700 and spent Rs 40300 on its repairs.
To make a profit of 5%, she should sell the house for Rs________
48) If 20 lemons are bought for Rs 10 and sold at 5 for three rupees,
then________ in the transaction is ________%.
49) Narain bought 120 oranges at Rs 4 each. He sold 60 % of the oranges at Rs 5
each and the remaining at Rs 3.50 each. His ________ is ________%.
50) A fruit seller purchased 20 kg of apples at Rs 50 per kg. Out of these, 5% of
the apples were found to be rotten. If he sells the remaining apples at Rs 60
per Kg, then his ________% is ________.
51) Interest on Rs 3000 at 10% per annum for a period of 3 years is ________.
52) Amount obtained by depositing Rs 20,000 at 8 % per annum for six
months is ________.
53) Interest on Rs 12500 at 18% per annum for a period of 2 years and 4 months
is ________.
54) 25 ml is _________ per cent of 5 litres.
55) If A is increased by 20%, it equals B. If B is decreased by 50%, it equals C. Then
__________ % of A is equal to C.
56) Interest =
×
×
, where
T is ____________ R% is ____________ and P is ____________.
57) The difference of interest for 2 years and 3 years on a sum of Rs 2100
at 8% per annum is _________.
58) To convert a fraction into a per cent, we _________ it by 100.
59) To convert a decimal into a per cent, we shift the decimal point two places to
the _________.
60) The_________ of interest on a sum of Rs 2000 at the rate of 6% per
annum for 1 years and 2 years is Rs 420.
61) When converted into percentage, the value of 6.5 is _________ than 100%.
State whether the statements are True or False.
62) = 66 %.
63) When an improper fraction is converted into percentage then the answer can
also be less than 100.
64) 8 hours is 50% of 4 days.
65) The interest on Rs 350 at 5% per annum for 73 days is Rs 35.
66) The simple interest on a sum of Rs P for T years at R% per annum is
given by the formula: Simple Interest =
67) 75% = .
× ×
.
68) 12% of 120 is 100.
69) If Ankita obtains 336 marks out of 600, then percentage of marks obtained by
her is 33.6.
70) 0.018 is equivalent to 8%.
71) 50% of Rs 50 is Rs 25.
72) 250 cm is 4% of 1 km.
73) Out of 600 students of a school, 126 go for a picnic. The percentage of
students that did not go for the picnic is 75.
74) By selling a book for Rs 50, a shopkeeper suffers a loss of 10%. The cost
price of the book is Rs 60.
75) If a chair is bought for Rs 2000 and is sold at a gain of 10%, then selling price
of the chair is Rs 2010.
76) If a bicycle was bought for Rs 650 and sold for Rs 585, then the percentage of
profit is 10.
77) Sushma sold her watch for Rs 3320 at a gain of Rs 320. For earning a gain of
10% she should have sold the watch for Rs 3300.
78) Interest on Rs 1200 for 1 years at the rate of 15% per annum is Rs 180.
79) Amount received after depositing Rs 800 for a period of 3 years at the rate of
12% per annum is Rs 896.
80) Rs 6400 were lent to Feroz and Rashmi at 15% per annum for 3 years and 5
years respectively . The difference in the interest paid by them is Rs 150.
81) A vendor purchased 720 lemons at Rs 120 per hundred.10% of the lemons
were found rotten which he sold at Rs 50 per hundred. If he sells the
remaining lemons at Rs 125 per hundred , then his profit will be 16%.