Class 7 Maths Notes for Comparing Quantities

NOTES

CLASS 7
MATHS

Study Material

DOWNLOAD PDF

COMPARING QUANTITIES
I. Concept and Result
(i)Ratio - Ratio compares two or more things of the same kind. Suppose when comparing of
two quantities of the same kind like height of Raju is 120 cm and that of monu is 80 cm. If we
want to compare it by division then
Raju′s height 120cm 3
= 80cm = 2= 3 : 2
Monu′s he ight
3
Raju's height = 2 X Monu‖s height
So ratio of two quantities of same kind and in the same measurement (units) is a fraction that
shows how many times the one quantity of the others. It is denoted by (:)
e.g. Ratio of two quantities a andb is written as a : b. It has no unit.
Percentage- Percent as the name suggests the amount or part of anything out of 100 parts or
5 1
per 100 or for every 100 and it is denoted by sign%. 5% =100 = 20
Profit or Loss- In daily life we come across situation where we either purchase or sell
something .
Cost Price ( CP) - Price at which object is bought or cost of shopkeeper in purchasing article
including fair, repair, etc.
Selling Price (S.P.) - The price at which the article is sold to the customer.
Three conditions arises/during the selling/buying processes
(i) SP > CP i.e. S.P. – C.P. > zeroi.e. profit
Profit
Profit = S.P. – C.P., profit % = C.P. X 100
(ii)C.P.>S.P. i.e.C.P.-S.P.>0 i.e. ioss
Loss
Loss= C.P.- S.P. , Loss%= C.P. X100
(III) S.P. = C.P. i.e. S.P. –C.P.=0
No profit no loss.
MRP means maximum retail price or marked of the article.
100+profit 100−loss
S.P. = ( ) x C.P. Or ( ) x C.P.
100 100
100 100
C.P.= (100+profit )X S.P. OR (100−loss )X S.P.
Simple Interest -It is used in landing/ borrowing money from either money lender or any
financial institution.
Three things are important
Principal It is the amount lent/ borrowed by a lender/ or from borrower. It is denoted by P.
Time The duration for which money lent/ borrowed. It is denoted by t.
RateRate of interest on which money is lent / borrowed. it is denoted by r and in the form of
percentage
PRT
Simple Interest = 100 , Amount (A) = P+S.I.

67

(MCQs – 4 Questions)
Q1 Find the ratio of 9m to 27cm.
(a)100:3 (b) 3:1100 (c) 3:100 (d) 30:10
1
Q2 Convert the given fractional numbers to percent 8.
(a)125% (b) 1.25%(c) 12.5%(d) 1250%
Q3 Find the whole quantity if 40% of it is 500 km.
(a)1200km (b) 1250km (c)1500km (d) 1000km
Q4 The population of a city decreased from 25,000 to 24,500. Find the percentage decrease.
(a)3% (b) 4% (c) 5%(d) 2%
(Case Based Question)
Read the paragraph carefully and answer the questions
For Diwali celebration Mayank needs to buy various kinds of sweets to gift his friends and
relatives. The rate list is as follows
Kaju Burfi (400 g) - Rs 600
Milk Cake (400 g) - Rs 450
Gulab Jamun (1 kg) - Rs 250
Kaju Roll (400 g) - Rs 900 (Do any four)
Q1. Mayank's friend gifted him 1 kg milk cake ,if he want to gift him Kaju Burfi of equal price
,then approximately how much kg of Kaju Burfi he have to gift? what is the ratio of price of
milk cake and Kaju Burfi?

A. 1kg, 450:700 B. 750 g,450:750 C. 850 g,450:850 D. 725 g,450:650
Q 2. Approximately how many kg of Gulab Jamun can be purchased in the price of 400 g Kaju
Roll ?
A. 4 kg B. 3 kg C. 2 kg D. 5 kg
Q 3. If Mayank purchased 400 g Kaju Roll and 1.5 kg Gulab Jamun ? Howmuch money he has
to pay to sweet seller ?
A. Rs 1225 B. Rs 1275 C. Rs 1245 D. Rs 1250
Q 4. Is the cost of 1 kg Gulab Jamun and 300g Kaju Roll together less than the cost of 250 g
Kaju Burfi and 400g Milk Cake together? Write both the prices in the ratio?

A. NO, 925:825 B. Yes, 900:800 C. Both are equal, 905:805D. Can't say,950:850
Q 5. The ratio of cost of 1 kg milk cake to 1kg Kaju Barfi. *

A. 1100: 1000 B. 1025 : 1100 C. 1125 : 1500 D. 900 : 1100

68

(Short answer type question:3)
Q1 Convert the given decimal fractions to percents 0.65.
Q2 Find 75% of1kg (gm)
Q3 25 ml is -------------- per cent of 5 liters.
(Long answer type question:2)
Q1 If x and y shared Rs 1100 in the ratio 1:10 , how much did x get?
Q2 In what time will Rs 4000 give an interest of Rs500 at 5% p.a.?

(Questions for Practice)

(i)MCQs
Q1 Convert the given decimal fractions to percents 0.02.
(a)3% (b) 4% (c) 5% (d) 2%
Q2 Find 1% of 1hour (minutes)
3 4 6 7
(a)5 (b) 5 (c) 5 (d) 5
Q3 15kg is ----------------% of 50kg.
(a)20% (b) 40% (c) 50% (d) 30%
Q4 The interest on Rs 30,000 for 3 years at the rate of 15% per annum is
(a)Rs 4,500 (b) Rs 9,000 (c)Rs 18,000 (d) Rs 13,500
Q5 The ratio 3:8 is equal to
(a)3.75% (b) 37.5% (c) 0.375% (d) 0.0375%
Q6 225% is equal to
(a)9:4 (b) 4:9 (c) 3:2 (d) 2:3
Q7 I bought a T.V. for Rs 10,000 and sold it at a profit of 20%.How much money did I get for it ?
(a)Rs20,000 (b)Rs 11,000 (c) Rs 15,000 (d) Rs 12,000
Q8 What sum of money earned Rs 90 as simple interest in 4 years at the rate of 5% ?
(a)Rs350 (b) Rs450 (c) Rs 550 (d) Rs 650
Q9 Amina buys a book for Rs 275 and sells it at a loss of 15% . How much does she sell it for.
(a)Rs233.25 (b) Rs233.50 (c) Rs233.75 (d) Rs233.35
1
Q10 Express 333 % as a ratio in the lowest form.
(a)1:3 (b) 3:1 (c) 33:1 (d) 1:33

(ii) Short answer type questions

Q1 Find ratio of 30 days to 36 hours.
Q2 Convert the given fractional numbers to percent 2.1.
Q3 Find the whole quantity if 70% of it is 14 minutes.
Q4 Meeta saves Rs 400 from her salary. If this is 10% of her salary. What is her salary?
Q5 A skirt bought for Rs250 and sold at Rs150 Find profit or loss percent.
Q6 At what rate will Rs840 yield an interest of Rs210 in 3 years?

69

Q7 90% of x is 315 km, the value of x is
Q8 Savitri obtained 440marks out of 500 in an examination . She secured --------------% marks in
the examination.
Q9 0.018 is equivalent to
4
Q10 when expreesed as a percent is
5

Long answer type questions
Q1In how many years a sum of money will become 4 times at 6% simple interest per annum.
Q2 Convert each part of the ratio to percentage
2:3:5
Q3 A dealer buys a wrist watch for Rs225 and spends Rs15 on its repairs. If he sells the same for
Rs 300, find his profit percent.
Q4 What is the rate of annual simple interest at which a sum of money would double itself in 25
years?
25% of 50% of 100%
Q5 Solve 25x50
Q6 800kg of mortar consist of 55% sand, 33% cement and rest lime. What is the mass of lime in
mortar?

Case Based Questions
Q1 In a quarterly examination ,a student secured 30% marks and failed by 12 marks .In the same
examination another student secured 40% marks and got 28 more bare minimum marks to pass.
Find
(i) the maximum marks (ii) the pass percentage
Q2 Chalk contains calcium, carbon and oxygen in the ratio 10:3:12 .
(i) Find the percentage of carbon in chalk.
(ii) ) Find the percentage of calcium in chalk.
(iii) ) Find the percentage of oxygen in chalk.
(iv) If in a stick of chalk , carbon is 3gm, what is the weight of the chalk stick?
CHAPTER TEST 1 (20 Marks)
Section A (4 MCQs,1mark each)
Q1 Find the ratio of 9m to 27cm.
(a)100:3 (b) 3:1100 (c) 3:100 (d) 30:10
1
Q2 Convert the given fractional numbers to percent .
8
(a)125% (b) 1.25%(c) 12.5%(d) 1250%
Q3 Find the whole quantity if 40% of it is 500 km.
(a)1200km (b) 1250km (c)1500km (d) 1000km
Q4 The population of a city decreased from 25,000 to 24,500. Find the percentage decrease.
(a)3% (b) 4% (c) 5%(d) 2%
Section B (5 Questios 2Marks each)
Q1 Convert the given decimal fractions to percents 0.65.
Q2 Find 75% of1kg (gm)

70

Q3 25 ml is -------------- per cent of 5 liters.
Q4 In a city 30% are females ,40% are males and remaining are children . What percent are children.
25
Q5 If x% of 2 is 150, find the value of x.
Section C (2 Questions 3 Marks each)
Q1 If 20% of x is same as 30% of y , what percentage of x is y?
Q2 What is the rate of annual simple interest at which a sum of money would double itself in 25
years?

Test 2 (30 Marks)
Section A (6 MCQ,s , 1 Mark each)
Q1 Find ratio of 30 days to 36 hours
(a) 20:1 (b) 200:1 (c) 200:10 (d) 200:100
5
Q2 Convert the given fractional numbers to percent 4.
(a)125% (b) 1.25%(c) 12.5%(d) 1250%
Q3 Find the whole quantity if 70% of it is 14 minutes.
(a)23 minutes (b) 20 minutes (c)25 minutes (d) 26 minutes
Q4 Meeta saves Rs 400 from her salary. If this is 10% of her salary. What is her salary?
a)Rs 400 (b) Rs 40 (c)Rs40,000 (d) Rs 4,000
Q5 A skirt bought for Rs250 and sold at Rs150 Find profit or loss percent.
(a)25% (b) 40%(c) 45%(d) 12%
Q6 At what rate will Rs840 yield an interest of Rs210 in 3 years?
(a)5.33% (b) 1.33%(c) 8.33%(d) 12.33%
Section B (6 Questios 2Marks each)
Q1 Find the whole quantity if 8% of it is 40 liters.
Q2 Out of 15,000 voters , 60% voted. Find the percentage of voters who did not vote.How many
actually did not vote?
Q3 In what time will Rs 4000 give an interestof Rs500 at 5% p.a.?
Q4 : What rate gives Rs 280 as interest on a sum of Rs 56000 in
2 Years.
Q5 A bicycle is purchased for Rs 1800 and is sold at a profit of 12%. Its selling price is?
Q6 Convert 0.07 in percent?
Section C (4 Questions 3 Marks each)
Q1 In a quarterly examination ,a student secured 30% marks and failed by 12 marks .In the same
examination another student secured 40% marks and got 28 more bare minimum marks to
pass.Find
(i) the maximum marks (ii) the pass percentage
Q2 Convert each part of the ratio to percentage
2:3:5
Q3 A dealer buys a wrist watch for Rs225 and spends Rs15 on its repairs. If he sells the same for
Rs 300, find his profit percent.

71

Q4 What is the rate of annual simple interest at which a sum of money would double itself in 25
years?

ANSWERS
MCQs Q1( a), Q2( c), Q3( b) Q4( d)
Case based questions Q1( B) , Q2( A) , Q3( B), Q4( A)
Short answer questions
75 X
(Q1) 0.65 x100% = 65% ,(Q2) 100 x1000 g = 750 gram , ( Q3) 100 x 5000 ml = 25 ml ,x =
0.5%
Long answer questions
(Q1) Let share of x is Rs a , share of y = rupees (1100 - a) , a: (1100 - a) = 1:10 (given) ,a =
100XS .I 100X500 1
100 , share of x is equal to rupees 100 , (Q2) T = = 4000 X5 = 2 2 years
PXR
MCQs
Q1( d), Q2( a) , Q3( d), Q4( d) , Q5( b), Q6( a), Q7( d), Q8( b), Q9( c), Q10( a)
Short answer type questions
30x24 70Xx
(Q1) = 20:1 , ( Q2) 2.1x100% = 210%‘ (Q3) 100 = 14 minutes , x= 20 minutes, (Q4)
36
10Xx
Let Meeta's salary=Rs x =400 ,x =Rs 4000, (Q5) C.P. = Rs 250 , S.P.= Rs 15 ,Loss= Rs
100
loss
100,L%= C.P. x100%= 40%
S.IX 100 210X100 1 90∗x
(Q6) P= Rs 840 ,S.I. = Rs210 ,T= 3years R = PXT = 840X3 =83 %, ( Q7) 100 =315,
x=350
440∗100% 4X100%
( Q8) = 88%, (Q9) 0.018x100%= 1.8%, (Q10) = 80%
500 5
Long answer type questions
PXRXT PX 6XT
(Q1) Let P= Rs P, A = Rs 4P, S.I= Rs 3P, S.I. , 3P = =50 Years
100 100
2X 100% 3 X 100% 5 X 100%
(Q2) 2+3+5= 10, =20%, = 30%, = 50%
10 10 10
(Q3) C.P.= Rs 225, overhead expenses= Rs 15 ,Total C.P.= Rs240,S P.= Rs 300, Profit=Rs 60
60 X 100%
P%= =25%, (Q4) Let P= Rs x, A= Rs2x, S.I.= 2x- x= Rs x, T=25years ,R =
240
S.I X 100
= 4%
PXT
25X50X100X1 1
(Q5) 100 X 100 X100 X25 X 50 =10000 =0.0001
(Q6) Percentage of sand= 55% , Percentage of cement= 33% , Percentage of lime= 100-88=
12%

72

12 X 800
Mass of lime in 800kg= = 96kg
100
Case based questions
3X
(Q1) Let the maximum marks be X .First student secured 30% of X = 10 marks ,he fails by 12
3X 2X
marks ,so pass marks = 10 + 12 ,Second student secured 40% of X = marks. Since he gets
5
2X 3X 2X
28 marks more than pass marks, pass marks = 5 - 28 marks, + 12 = - 28 ,Maximum
10 5
132 X 100
marks= 400 ,Pass marks = 132 ,pass percentage = = 33%
400
(Q2) Chalk contains calcium ,carbon, oxygen in the ratio 10 :3: 12 ,now 10 + 3 + 12 = 25
3 X 100
percentage of carbon = =12% similarly percentage of calcium and oxygen 40% and
25
48%. Let the weight of chalk stick =X gram , 12% of X =3 ,X =25 gram
Test 1
Section A
Q1(a), Q2(c), Q3(b), Q4(d)
Section B
75 X
(Q1) 0.65x100= 65% , (Q2) 100 x1000g =750g , (Q3) Let 25ml be x% of 5liters , 25 = 100 x
5000, X= 0.5%
x X 25
(Q4) Percentage of children= [100- (30+40)]= 30% , (Q5) 100 X2 =150, X= 1200
Section
20 X x 30 X y 2x 200
(Q1) 100 = 100 , = y, Let x= 100%, Y= 3 , (Q2) Done
3
TEST 2 Section A
MCQs Q1 (a) ,Q2 (b) , Q3 (b) ,Q4 (d), Q5 (b) , Q6 (c)
Section B
8Xx
Q1 100 = 40 liters , Q2 No. of voters who did not vote = 40% of 15000 = 6000,
S.I.X100 500X100 1
Q3 P= Rs 4000 , S.I.=Rs500 , R =5% , T= = 4000 X5 = 22 Years
PXR
PXRXT 56000 X R X 2 P P
Q4 S.I.= , 280 = = 0.25% , Q5 Profit% = C.P.X100% , 12= 1800 X100,
100 100
P=Rs 216 , S.P= Rs 1800+ Rs 216 =Rs 2016 , Q6 0.07X 100% =7%
Section D Done earlier.

73

RATIONAL NUMBERS
Important Facts and Concepts:
𝑝
A number that can be expressed in the form𝑞 , where p and q are integers and q ≠ 0, is called a
rational number.
All integers and fractions are rational numbers.
If the numerator and denominator of a rational number are multiplied or divided by a non-zero
integer, we get a rational number which is said to be equivalent to the given rational number.
Rational numbers are classified as positive, zero or negative rational numbers. When the
numerator and denominator both are positive integers or both are negative integers, it is a
positive rational number. When either the numerator or the denominator is a negative integer, it
is a negative rational number.
The number 0 is neither a positive nor a negative rational number.
There are unlimited number of rational numbers between two rational numbers.
A rational number is said to be in the standard form, if its denominator is a positive integer and
the numerator and denominator have no common factor other than 1.
Two rational numbers with the same denominator can be added by adding their numerators,
keeping with the same denominator.
Two rational numbers with different denominators are added by first taking the LCM of the two
denominators and then converting both the rational numbers to their equivalent forms having the
LCM as the denominator and adding them as above.
While subtracting two rational numbers, we add the additive inverse of the rational number to be
subtracted to the other rational number.
𝐏𝐫𝐨𝐝𝐮𝐜𝐭 𝐨𝐟 𝐧𝐮𝐦𝐞𝐫𝐚𝐭𝐨𝐫𝐬
• 𝐏𝐫𝐨𝐝𝐮𝐜𝐭 𝐨𝐟 𝐫𝐚𝐭𝐢𝐨𝐧𝐚𝐥 𝐧𝐮𝐦𝐛𝐞𝐫𝐬 =
𝐏𝐫𝐨𝐝𝐮𝐜𝐭 𝐨𝐟 𝐝𝐞𝐧𝐨𝐦𝐢𝐧𝐚𝐭𝐨𝐫𝐬
𝒑 𝒒
• The reciprocal of a non-zero rational number 𝒒 𝒊𝒔 𝒑 .
• To divide one rational number by the other non-zero rational number, we multiply the first
rational number by the reciprocal of the other.
−45
EXAMPLE 1 Reduce 30 to the standard form.
−45 3×3×5 5
Solution: 30 = − 2×3×3 = − 2
4 16
EXAMPLE 3: Do −9 and − 36represent the same rational number?
4 4 −16 −16 4 4
Solution: Yes, because −9 × 4 = 36 , ÷4 = −9
36
EXAMPLE 3 List three rational numbers between – 2 and – 1.
10 20 10 19 18 17
Solution:−2 × 10 = − 10 , −1 × 10 , Any three numbers are, − 10 , − 10 , − 10
SHORT ANSWER QUESTIONS:
55
Q1. Reduce 66 into the standard form.
55 11 5
Solution:66 ÷ 11 = 6
3
Q2. Express 4 as a rational number with denominator as −80
Solution:−80 ÷ 4 = −20

74

3 −20 − 60
So, 4 × −20 = −80
15 11
Q3. Find the product of ×
22 5
15 11 3×5 11 3
Solution:22 × 5 = × 5 =2
2×11
2 1
Q4. Simplify:5 − 2
Solution: LCM of 2 𝑎𝑛𝑑 5 is 10
2 2 4
× =
5 2 10
1 5 5
× =
2 5 10
4 5 4−5 1
So, 10 − 10 = 10 = − 10

LONG ANSWER QUESTIONS:
Q1.List five rational numbers between −4 𝑎𝑛𝑑 − 3.
6 24
Solution:−4 × 6 = − 6
6 −18
−3 × = −
6 6
five rational numbers between −4 𝑎𝑛𝑑 − 3 are,
19 20 21 22 23
− ,− ,− ,− ,−
6 6 6 6 6
29 30
Q2. Solve: 4 − 7
Solution: LCM of 4 𝑎𝑛𝑑 7 𝑖𝑠 28.
29 7 203
× =
4 7 28
23 7 161
× =
4 7 28
So,
203 161 203 − 161 42 2 × 3 × 7 3
− = = = =
28 28 28 28 2 × 2 × 7 2
PRACTICE QUESTIONS:
MCQ:
Q1. In the standard form of a rational number, the common factor of numerator and denominator
is always:
(a) 0 (b) 1 (c) – 2 (d) 2
Q2: Which of the following rational numbers is equal to its reciprocal?
1
(a) 1 (b) 2 (c) 2 (d) 0
Q3. How many rational numbers are there between two rational numbers?
(a) 1 (b) 0 (c) unlimited (d) 100
Q4. In the standard form of a rational number, the denominator is always a
(a) 0 (b) negative integer (c) positive integer (d) 1

75

Study Materials
Notes

Model Papers Class 6 Notes

Sample Papers Class 7 Notes
Half Yearly Sample Papers Class 8 Notes

Class 9 Notes
Important Resources
Class 10 Notes
Periodic Table
Class 11 Notes
Writing Skills / Formats

Maps of India / World Class 12 Notes

Books and Solutions

NCERT Books
NCERT Book Solutions
HC Verma Chapter Wise Solutions
RD Sharma Solutions
CGBSE Solutions