Chapter 8: Comparing Quantities
Exercise 1:
(Multiple Choice Questions and Answers 1-23)
In questions 1 to 23, there are four options,
out of which one is correct. Write the correct one.
Question: 1
of is
a.
b.
c.
d.
Solution
(d)
of
Therefore, of is .
Question: 2
Gayatri’s income is per year. She pays of this as house rent and of the remainder on her child’s education. The
money left with her is
a.
b.
c.
d.
Solution
(c)
Given, Gayatri’s income
Money paid as house rent = of
Remaining amount
Money spent on child’s education of
Money left with Gayatri
Question: 3
The ratio of Fatima’s income to her savings is .
The percentage of money saved by her is
a.
b.
c.
d.
Solution
(a)
Given ratio of income to savings of Fatima
Here, we need to find out the percentage of money
saved by Fatima.
Let the income and her savings
Percentage of money saved by Fatima
Question: 4
is equal to
a.
b.
c.
d.
Solution
(b)
Question: 5
In a scout camp, of the scouts were from Gujarat State and of these were from Ahmedabad. The percentage
of scouts in the camp from Ahmedabad is:
a.
b.
c.
d.
Solution
(c)
Let the number of scouts in
scout camp
The number of scouts from Gujarat of
Number of scouts from Ahmedabad of
Percentage of scouts from Ahmedabad
Question: 6
What percent of is ?
a.
b.
c.
d.
Solution
(a)
Let the percentage
be
Option (a) is the correct one
Question: 7
is equal to
a.
b.
c.
d.
Solution
(c)
We have,
In percentage,
Question: 8
The ratio is equal to
a.
b.
c.
d.
Solution
(b)
Given, ratio
In percentage,
Question: 9
is equal to
a.
b.
c.
d.
Solution
(a)
We have, in fraction,
Required ratio
Question: 10
A bicycle is purchased for and is sold at a profit of .
Its selling
price is
a.
b.
c.
d.
Solution
(b)
Given, cost price of bicycle and profit
As we know, profit percentage can be calculated as,
Profit
Profit
SP CP Profit
Hence, selling price of bicycle is
Question: 11
A cricket bat was purchased for and was sold for .
Then profit
earned is
a.
b.
c.
d.
Solution
(a)
Given, cost price of bat
Selling price of bat
Profit SP CP
We know that profit percentage is given as,
Profit
Hence, profit earned is
Question: 12
A farmer bought a buffalo for and a cow for .
He sold the
buffalo at a loss of but made a profit of on the cow. The net result of the transaction
is
a.
loss of
b.
profit of
c.
loss of
d.
profit of
Solution
(c)
CP of buffalo
Loss
Loss
Loss
SP CP Loss
CP of cow
Profit
Profit
Profit
SP CP Profit
Total CP of buffalo and cow
Total SP of buffalo and cow
Net loss CP SP
Question: 13
If Mohan’s income is more than Raman’s income, then Raman’s income
is less than Mohan’s income by
a.
b.
c.
d.
Solution
(c)
Let the Raman’s income be .
Mohan’s income is more than Raman’s income.
Then, Mohan’s income of
Percentage of Raman’s income less than Mohan’s income
Question: 14
The interest on for years at the rate of per annum is
a.
b.
c.
d.
Solution
(d)
Given,
We know that,
Question: 15
Amount received on for years at the rate of per annum is
a.
b.
c.
d.
Solution
(b)
Given,
Now, amount
Question: 16
Interest on for month at the rate of per annum is
a.
b.
c.
d.
Solution
(c)
Given,
Question: 17
Rajni and Mohini deposited and in a company at the rate of per annum for years and years respectively. The difference of the
amounts received by them will be
a.
b.
c.
d.
Solution
(d)
Interest received by Rajni after 3 years,
I
And total amount received will be,
Interest received by Mohini after years,
I
And total amount received will be,
Difference in amounts
Question: 18
If of is then the value of
a.
b.
c.
d.
Solution
(b)
Given,
of
Question: 19
On selling an article for a dealer lost .
The cost price of the article is
a.
b.
c.
d.
Solution
(d)
Given, SP of an article is and loss per cent
We know that, loss per cent
Question: 20
is equal to
a.
b.
c.
d.
Solution
We have,
In percentage,
Question: 21
The sum which will earn a simple interest of in years at
per annum is
a.
b.
c.
d.
Solution
(c)
Given, and
Question: 22
The
per cent that represents the unshaded region in the figure.

a.
b.
c.
d.
Solution
(c)
Total parts
Shaded
parts
Percent
of shaded parts
Then,
percent of un-shaded parts
Hence,
the per cent that represents the un-shaded region is
Question: 23
The per cent that represents the shaded region in
the figure is

a.
b.
c.
d.
Solution
(a)
Total parts
Shaded parts
Percent of shaded parts
Hence, the per cent that represents the shaded region is
In each of the questions 24 to 59, fill in the blanks to make the
statements true.
Question: 24
______
Solution
Given ratio
In percentage
Question: 25
_______: ______
Solution
Given percentage
In fraction,
Ratio
Question: 26
of _____.
Solution
We have, of
Question: 27
of _____.
Solution
We have, of
Question: 28
_____
Solution
We have,
In percentage,
Question: 29
_____
Solution
We have,
In percentage,
Question: 30
A
________ with its denominator is called a per cent
Solution
A fraction
with its denominator is called a per cent.
Question: 31
is ______ of
Solution
Let of be
Then,
Hence, is of
Question: 32
Weight of Nikhil increased from to .
Then, the increase in weight is _____ .
Solution
Given, Initial weight of Nikhil
After increase in weight, weight became Increase in weight
Percentage
increase of weight
Question: 33
In a class of students, were absent on one day. The number of students
present on that day was ________.
Solution
Given, Total number of students in the class
Absent percentage on one day
Percentage of students present on that day
Number of students present on that day of
So, the number of students present on that day, was
Question: 34
Savitri obtained marks out of in an examination. She secured _______ marks in the examination.
Solution
Marks obtained by Savitri out of
Percentage of marks obtained
Hence, Savitri secured marks in the examination
Question: 35
Out of a total deposit of in her bank
account, Abida withdrew of the deposit. Now the balance in her account
is ______.
Solution
Total deposit
Amount withdrawn of
Balance in the account
Question: 36
________ is more than .
Solution
Let number be
It is given that is more than
Therefore, according to question
of
Question: 37
John sells a bat for and suffers
a loss of . The cost price of the bat is ________.
Solution
Given, SP of bat and loss
We know that, CP SP Loss
Hence, cost price of the bat is
Question: 38
If the price of sugar is decreased by then
the new price of sugar
originally costing will
be ________.
Solution
Original price of sugar
Given that, price of sugar is decreased by
So, new price of sugar Original price of original price
of
Question: 39
Mohini bought a cow for and
sold it at a loss of . The selling price of the cow is ________.
Solution
Given, CP of cow and loss
We know that, SP CP Loss
Hence, the selling price of the cow is
Question: 40
Devangi buys a chair for and
sells it for . She earns a profit of ________ in the
transaction.
Solution
Given, CP of a chair and SP of a chair
Since, SP CP
Profit SP CP
Now, Profit
Hence, Devangi’s profit is
Question: 41
Sonal bought a bed sheet for and
sold it for . Her ________ is
________.
Solution
Given, CP of a bed sheet and SP of a bed sheet
Since, SP CP
Profit SP CP
Now, profit
Hence, Sonal’s profit is
Question: 42
Nasim bought a pen for and
sold it for . His ________ is
________.
Solution
Given, CP of a Pen and SP of a pen
Since, SP CP
Loss CP SP
Now, Loss
Hence, Nasim’s loss is
Question: 43
Aahuti purchased a house for and
spent on its
repairs. To make a profit of , she should sell the house for ________.
Solution
Given, CP of house
And amount spent on repairing
So, total CP of house
Profit
Question: 44
If lemons
are bought for and
sold at for
three rupees, then ________ in the transaction is ________ .
Solution
CP of lemons
By applying unitary method,
If SP of lemons is
Then, SP of lemon
SP of lemons
Now, CP and SP
Since, SP CP
Profit SP CP
Now, profit
Hence, profit is
Question: 45
Narain bought oranges at each.
He sold of the
oranges at each
and the remaining at each.
His ________ is ________ .
Solution
CP of orange (given)
CP of oranges
Now, of oranges
SP of oranges
And SP of remaining oranges
Total SP of oranges
Since, SP CP
Profit SP CP
Now,
Profit per cent
Hence, profit is
Question: 46
A fruit seller purchased of
apples at . Out of these, of the
apples were found to be rotten. If he sells the remaining apples at , then his _________is _________ .
Solution
Price for per kg apples
Total weight of purchased apples
Since, were rotten, so weight of good apples of (rotten)
Also, he sells apples at per kg
Total SP
Cost price of apples
Profit SP CP
Now, Profit
So, his profit is
Question: 47
Interest on at per
annum for a period of years
is ________.
Solution
Given, and
Hence,
interest is
Question: 48
Amount obtained by depositing at per
annum for six months is ________.
Solution
Amount
deposited
Rate of interest
Time period months
Amount
received Principal Interest
Question: 49
Interest on at per
annum for a period of years
and months
is ________.
Solution
Given, and
months
We know that,
Question: 50
is
_________ per cent of litres.
Solution
Let be of
Then, of
[Converting litre into millilitre]
Hence, is of
Question: 51
If A is increased by it
equals B. If B is decreased by it
equals C. Then __________ of A
is equal to C.
Solution
Given, if is increased by then it is equal to
of
(i)
If B is decreased by then it is equal to C.
of
(ii)
On comparing eq. (i) and (ii), we get
In percentage
Hence, of A is equal to C.
Question: 52
Interest where
is
____________
is
____________ and
is
____________.
Solution
Here, T is time period, is rate of interest and P is Principal.
Question: 53
The difference of interest for years and years on a sum of at per annum is _________.
Solution
Given, and
For,
For
Difference between both interests
Question: 54
To convert a fraction into a per cent, we _________
it by .
Solution
To convert a fraction into a per cent, we multiple it by
Question: 55
To convert a decimal into a per cent, we shift the
decimal point two places to the _________.
Solution
To convert a decimal into a per cent, we shift the
decimal point into places to the right.
Question: 56
The _________ of interest on a sum of at the rate of per annum for years and years is .
Solution
Given, and
Now,
For
The sum of both interests is
Question: 57
When converted into percentage, the value of is _________ than .
Solution
In percentage,
When converted into percentage, the value of 6.5 is
more than
In questions 58 and 59 copy
each number line. Fill in the blanks so that each mark on the number line is
labelled with a per cent, a fraction and a decimal. Write all fractions in
lowest terms.
Question: 58

Solution
Percentage Fraction
Decimal
Now, according to the formula, we have
Percentage
|
Fraction
|
Decimal
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Question: 59

Solution
Percentage Fraction
Decimal
Now, according to the formula, we have
Percentage
|
Fraction
|
Decimal
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
True/False
In questions to state whether the statements are true of False.
Question: 60
Solution
True
Given fraction
In percentage,
Question: 61
When an improper fraction is converted into
percentage then the answer can also be less than .
Solution
False
Let’s consider, an improper fraction
In percentage,
Hence, when an improper fraction is converted into
percentage, then the answer is always greater than
Question: 62
hours
is of days.
Solution
False
Let be of days
Then, of days
Hence, is of days
Question: 63
The interest on at per annum for days is .
Solution
False
Given,
And days
Question: 64
The simple interest on a sum of for T years at per annum is given by the formula: Simple Interest
=
Solution
True
Simple Interest
It can also be written as, SI
Question: 65
Solution
False
In fraction, can be written as
Question: 66
of is .
Solution
False
of
Therefore, of is
Question: 67
If Ankita obtains marks out of then percentage of marks obtained by her is
Solution
False
Marks obtained by Ankita out of
Percentage of marks
Hence, Ankita got marks.
Question: 68
is
equivalent to
Solution
False
In percentage, can be written as,
Hence, is equivalent to
Question: 69
of is
Solution
True
Since, of
Hence, of is
Question: 70
is of
Solution
False
Now, of
Hence, of
Question: 71
Out of students of a school, go for a picnic. The percentage of students
that did not go for the picnic is
Solution
False
Total number of students in school
Number of students who went for picnic
Number
of students who did not go for picnic
Percentage of students who did not go for picnic,
Therefore, of students did not go for picnic.
Question: 72
By selling a book for ,
a shopkeeper suffers a loss of .
The cost price of the book is .
Solution
False
SP of book
Loss per cent on book
Loss per cent
Loss per cent
Hence, the cost price of the book is
Question: 73
If a chair is bought for and is sold at a gain of then selling price of the chair is .
Solution
False
Given, and Profit per cent
Profit per cent
Profit
10
Hence, SP of chair is
Question: 74
If a bicycle was bought for and sold for ,
then the percentage of profit is .
Solution
False
Given, CP of bicycle and SP of bicycle
Since, CP SP
Loss CP SP
Now, Loss per cent
Hence, Loss per cent is
Question: 75
Sushma sold her watch for at a gain of .
For earning a gain of she should have sold the watch for
Solution
True
Given, SP of watch
Profit on SP
CP SP Profit
Now, for earning profit ,
we need to find new SP.
Profit per cent
Profit
Profit per cent
Question: 76
Interest on for years at the rate of per annum is
Solution
False
Given, and
So, interest is
Question: 77
Amount received after depositing for a period of years at the rate of per annum is
Solution
False
Given, and
So, interest is
Hence, the amount received will be
A = P+ I
=
Question: 78
were
lent to Feroz and Rashmi at per annum for and years respectively. The difference in the
interest paid by them is
Solution
False
As per the question, Feroz borrowed for at per annum.
Here, and
Rashmi borrowed for at
Here,
Difference between interests
Hence, the difference in interest, paid by them is
Question: 79
A vendor purchased lemons at per hundred. of the lemons were found rotten which he sold
at per hundred. If he sells the remaining lemons
at per hundred, then his profit will be .
Solution
False
As per the question, cost price of lemons
Cost price of lemon
And cost price of lemons
Now, according to question, of the lemons were rotten.
of lemons lemons
Selling price of rotten lemons
Selling price of rotten lemon
And selling price of rotten lemons
Also, selling price of good lemons per hundred
& selling price of good lemons
Now, total selling price of lemons
As, SP CP
Therefore, vendor will bear loss.
Question: 80
Find the value of if
a. of is
of is
of is
of marks is
Solution
a. of is (given)
of is (given)
of is (given)
of marks is (given)
Question: 81
Imagine that, a grid has value and that this value is divided evenly among
the small squares. In other words, each small square is worth Use a new grid for each part of this problem
and label each grid “Value : ”.

a. Shade of the grid. What is of Compare the two answers.
What is the value of squares?
Shade of the grid. What is of Compare the two answers.
What is the value of of the grid?
Solution
a. We have to shade of the grid i.e., th part of grid th part of grid covers squares. Since, one square =
So,
total value of such squares
Now, of

Hence,
the above values are equal
Value of squares
of the grid means squares. So we will shade squares

Total
value these squares
Now,
of
Hence,
the above two values are equal.
Value
of grid
Value of of the grid
Question: 82
Express as a per cent.
Solution
In percentage, can be written as
Question: 83
Express as a per cent.
Solution
In percentage, can be written as
Question: 84
Express as a per cent.
Solution
In percentage, can be written as
Question: 85
Express as fraction in its lowest term.
Solution
In fraction, can be written as
Question: 86
Express as a ratio in the lowest term.
Solution
can be written as
For ratio in lowest term, can be
written as
Question: 87
Express as a ratio in the lowest form.
Solution
Given,
For ratio in lowest term,
Question: 88
Express as a ratio in the lowest form.
Solution
For the ratio in lowest term
Question: 89
Sachin and Sanjana are calculating of
Now calculate of using both the ways described above. Which way
do you find easier?
Solution
First way,
of
Second way,
of
Hence, second way is the easier to find the percentage.
Question: 90
Write as a percent.
Solution
In percentage, can be written as,
[to
convert in per cent, multiply by ]
Question: 91
Write as a percent.
Solution
In percentage, can be written as,
Question: 92
What is of
Solution
We need to
find, of ,
which can be written as,
Question: 93
What is of
Solution
We need to find of ,
which can be written as,
Question: 94
What is of
Solution
We need to find of ,
which can be written as,
Question: 95
What per cent of hour is minutes?
Solution
Let of h be min.
Then, min.
min min
Therefore, of hr. is min.
Question: 96
What per cent of day is minute?
Solution
Let of day is min
Then, day min
h min
min min
Therefore, of day is min
Question: 97
What per cent of is metres?
Solution
Let of km is m
Then, km m
m m
Therefore, of km is m
Question: 98
Find out of
Solution
We have to find, of kg, which can be written as,
kg
Hence, of is 2 kg
Question: 99
What percent of is
Solution
Let is
Then,
Hence, of is
Question: 100
of the
population of a town are men and are women. What is the percentage of children?
Solution
Given, percentage of men in town
Percentage of women in town
So, percentage of children in town will be
Hence, of the population of a town are children
Question: 101
The strength of a school is If of the students are girls then how many boys
are there in the school?
Solution
According to the question,
The strength of school
Percentage of girls in school
Percentage of boys in school
Number of boys in school of 2000, i.e
Hence, number of boys in school are
Question: 102
Chalk contains calcium, carbon and oxygen. Find the amount of carbon and calcium
(in grams) in of chalk.
Solution
Given, percentage of calcium in chalk
Percentage of carbon in chalk
Percentage of oxygen in chalk
Weight of chalk
Amount of carbon in chalk of
Amount of calcium in chalk of
Therefore, amount of carbon & calcium are and respectively.
Question: 103
of
mortar consists of sand, cement and rest lime. What is the mass of lime
in mortar?
Solution
Given, percentage of sand in mortar
Percentage of cement in mortar
So, percentage of lime in mortar
Weight of mortar
Mass of lime in mortar of
Therefore, weight of lime in mortar is
Question: 104
In a furniture shop, tables were bought at the rate of per table. The shopkeeper sold of them at the rate of per table and the remaining at the rate of per table. Find her gain or loss percent.
Solution
Buying cost
of the tables C.P
Selling cost of the tables
S.P
Gain or loss S.P C.P,
Therefore,
Gain S.P C.P
Gain
Question: 105
Medha deposited of her money in a bank. After spending of the remainder, she has left with her. How much did she originally
have?
Solution
Let the total money Medha had