Percentage
Class 8th Mathematics West Bengal Board Solution
- I have Rs. 50 with me. I spent 12% of the sum of Rs. 50 to purchase a pen. Let’s work…
- It needs 120% tax to import a machine from abroad. Let’s work out the cost of the…
- Let’s calculate:(i) 15% of Rs. 80(ii) 12% of Rs. 215(iii) 118% of 37.8 metre(iv) 200%…
- (i) Rs. 2.25 out of Rs. 5(ii) 85g out of 17 kg(iii) 2.250 kg out of 0.72 quintal.…
- Let’s fill up the table below
- The ratio of hydrogen in water is 2:1. Let’s work out the percentage of hydrogen and…
- 1500 bottles were produced in a factory at Hridypur. Now 1695 bottles are produced…
- The quantity of Nitrogen, Oxygen and Carbon dioxide in the air is 75.6%, 23.04% and…
- Trisha has bought a book from the bookstall of Milan dada. Milan dada gave her…
- The length of each arm of a square was increased by 10%. Let’s work out the increase…
- We get a 15% discount if the bill for electricity is paid in time. My aunt got a…
- The price of sugar has increased by 20%. Let’s work out the percentage of decrease in…
- When water freezes into ice, it increases in volume by 10%. Let’s work out in…
- Due to use of high-yielding seed Utpalbabu has got 55% production hike in paddy…
- In a legislative election, 80% voters cast their votes and the winning candidate got…
- This year the students of Nandlal H.S school have passed 85% in Bengali, 70% in maths…
- The income of Amina Bibi was increased by 20% and later decreased by 20% Let’s work…
- The length of a rectangle is increased by 15% and the breadth is reduced by 15%. Let’s…
- The length, breadth and height of a room are 15m, 10m, 5m respectively. If the length…
- In annual sports, 20% of the students of took part in the 100m race. 15% of the…
Lets Work Out 11
Question 1.I have Rs. 50 with me. I spent 12% of the sum of Rs. 50 to purchase a pen. Let’s work out the amount I spent for purchasing the pen.
Answer:
Given: Amount = Rs 50
the percentage = 12%.
Tip: x% of y means 
In the question, it is said that the person spent 12% of the amount he/she possessed i.e.; Rs 50 on the pen.
Using the tip given above we can easily calculate the price of the pen.
Therefore,
Price of Pen
= Rs.6
Question 2.
It needs 120% tax to import a machine from abroad. Let’s work out the cost of the machine here after paying the tax if it costs Rs. 300000 in abroad.
Answer:
Given: import tax = 120%
cost of machine in abroad = Rs 300000
Tip: x% of y means .
In the question it is said that the machine has an import tax of 120%. Hence we need to calculate the import tax and add it to the actual cost of the machine abroad to get the final answer.
Therefore,
Cost of the machine after importing= Actual cost of machine abroad + Import tax.
Using the tip above we can easily calculate the import tax on the machine.
Therefore,
Import tax on the machine=
=Rs. 360000.
Now,
the cost of the machine after importing
= Actual cost of machine abroad + Import tax.
=300000+360000
=Rs.660000.
Question 3.
Let’s calculate:
(i) 15% of Rs. 80
(ii) 12% of Rs. 215
(iii) 118% of 37.8 metre
(iv) 200% of 48g
Answer:
(i)
Given: percentage 15% and money Rs.80
Tip: x% of y means .
Using the tip above we can easily get the amount after calculating the percentage on the given money.
Therefore, the answer is:
=1.5×8
=Rs. 12
(ii)
Given: percentage = 12%
Money = Rs.215
Tip: x% of y means .
Using the tip above we can easily get the amount after calculating the percentage on the given money.
Therefore, the answer is:
=Rs. 25.8
(iii)
Given: percentage = 15%
Distance = 37.8 m
Tip: x% of y means .
Using the tip above we can easily get the length after calculating the percentage on the given distance.
Therefore, the answer is:
=5.67 m
(iv)
Given: percentage = 200%
weight = 48 g.
Tip: x% of y means
Using the tip above we can easily get the weight after calculating the percentage on the given weight.
Therefore, the answer is:
=
=
=
g
Question 4.
(i) Rs. 2.25 out of Rs. 5
(ii) 85g out of 17 kg
(iii) 2.250 kg out of 0.72 quintal.
Answer:
(i)
Given: Amount = Rs 2.25
out of the amount of Rs. 5.
Tip: Percentage of x out of y is : 
%
Using the above tip we can easily calculate the required percentage of Rs.2.25 out of Rs. 5.
Therefore, the required answer is:
=
=
=
%
(ii)
Given: the weight whose percentage has to be calculated i.e; 85 g
out of the weight of 17 kg.
Tip: Percentage of x out of y is : %
Using the above tip we can easily calculate the required percentage of
85 g out of the weight of 17 kg.
Therefore, the required answer is:
=0.005×100
=0.5%
(iii)
Given: the weight whose percentage has to be calculated i.e; 2.250 kg
out of the weight of 0.72 quintal.
Tip: (i)Percentage of x out of y is : %
(ii) 1 quintal = 100 kg.
Using the above tip we can easily calculate the required percentage of 2.250 kg out of the weight of 0.72 quintal.
Using tip (ii)
0.72 quintal = 
kg=72 kg.
Using tip (i)
We get the desired percentage,
=0.03125×100
=3.125 %
Question 5.
Let’s fill up the table below
Answer:
Tip: Percentage to fraction:
divide by 100 and divide numerator by denominator.
The quotient is written as a whole number and the remainder is written as a fraction with it being the numerator and the previous denominator as the denominator in this case also.
final form: 
where k is the whole number
p is the remainder
q is the denominator both before and after division.
Decimal to fraction
Write the integer part of the decimal as the whole number in fraction.
The decimal part is then multiplied with appropriate power of ten and then adjusted by dividing with the same quantity below it.
Follow repeated division until 
form obtained where p and q have no factors in common.
Write the whole number and then the fraction obtained towards the right of it.
Fraction to percentage:
Multiply by 100.
Fraction to decimal:
Normal division, if recurring decimal occurs then give dot symbol above the digit that is recurring or dash symbol above the group of digits recurring.
Question 6.
The ratio of hydrogen in water is 2:1. Let’s work out the percentage of hydrogen and oxygen in water.
Answer:
Given : ratio of hydrogen: oxygen=2:1.
Tip: Fraction to Percentage conversion is done by multiplying with 100.
In the question we get to know the fraction or ratio between hydrogen and oxygen i.e; 2:1.
Hence, we can write Hydrogen occupies two parts in water
and Oxygen occupies one part.
But since water itself is only composed of hydrogen and oxygen
therefore,
Total parts of water = Parts of hydrogen + parts of oxygen.
= 2+1
=3 parts.
Therefore,
Fraction of water occupied by hydrogen
Fraction of water occupied by oxygen
Percentage of water occupied by hydrogen
=66.66%
percentage of water occupied by oxygen
=33.33%
Question 7.
1500 bottles were produced in a factory at Hridypur. Now 1695 bottles are produced there. Let’s work out the percentage of increase of production in that factory.
Answer:
Given: Previous production of bottles in the factory at Hridypur=1500
Present production of bottles in the factory at Hridypur=1695
Tip: increment percentage
From the data given in the question we can easily find out the increment due to the present production at the factory.
Therefore,
Increment in production= Present production - Previous Production
= 1695-1500
=195 bottles.
Now, by using the tip given we can easily get the required percentage.
Therefore,
Increment Percentage
=13%
Question 8.
The quantity of Nitrogen, Oxygen and Carbon dioxide in the air is 75.6%, 23.04% and 1.36%; Let’s work out quantity of each is 25 litres of air.
Answer:
Given: percentage of gases in air,
Nitrogen: 75.6%
Oxygen: 23.04%
Carbon dioxide: 1.36%
Tip: If x% of substance is present in a given quantity of y,
then the amount of substance present in y=
From the Question, we already know the percentage of the respective gases,
Therefore, by using the tip given, we can easily find out the required answer.
(Note that the percentage of the respective gases given in air does not change upon the quantity of air in which their amount has to be calculated.)
Amount of Nitrogen gas present
=18.9 ltr.
Amount of Oxygen gas present
=5.76 ltr.
Amount of Carbon dioxide present
=0.34 ltr.
Question 9.
Trisha has bought a book from the bookstall of Milan dada. Milan dada gave her discounts of 10% and 5% respectively. Let’s work out how much Trisha paid to Milan dada if the M.R.P of the book was Rs. 200.
Answer:
Given: MRP of the book=Rs.200
Discount given (i)=10%
Discount given (ii)=5%
Tip: The given discounts have to be calculated on a certain amount, and then the price has to be deduced from the amount to get the required answer.
If x% discount is given on y amount, then the discount amount is=
According to the question we see that there are two discounts.
On first look it may seem that we need to calculate 10%+5% i.e;15% discount on the MRP and then deduce it from MRP to get the answer, but that would be wrong.
In the question it is written that the discounts are given respectively i.e; the first discount (10%) has to be calculated on the MRP and deduce it to get the first price , then another 5% discount has to be calculated on this price and deduce it from this price to get the final answer.
Following what has been described above and the tip given we proceed as follows,
The amount or price after the first discount
=200-20
=Rs. 180(let us call it "price1")
Now, calculating the required answer:
=180-9
=Rs. 171
Question 10.
The length of each arm of a square was increased by 10%. Let’s work out the increase of the percentage of area by the Rule of Three.
Answer:
Given: percentage increment of each arm of the square.
Tip:(i) if y is increased by x% then the new value of y is 
(ii) Increment percentage
Let us assume that the length of each arm of the square is "a" unit length.
Using tip (i)
We calculate the new value of the arms of the square.
Therefore, the new value of the arms of the square is 
We know area of square = side × side
The area of the square when the arm length was “a “units = a× a = a2 unit square.
The area of the square when the arm length has changed to 
unit is
Therefore, the increment of the area is 
Therefore, the increment percentage is:
=21%
Question 11.
We get a 15% discount if the bill for electricity is paid in time. My aunt got a rebate of Rs. 54 paying the bill in time. Let’s work out the total amount of the bill.
Answer:
Given: the discount if electricity bill is paid in time=15%
The discount got by the aunt on the electricity bill by paying within time=Rs. 54.
Tip: if x% discount is given on y amount then the discount amount is
Let us assume that the total electricity bill is Rs. x.
Therefore, by using the data given in the question and the tip provided
we can easily figure out the total electricity bill amount by manipulating the discount amount equation given in tip.
From the tip provided, we can say,
or,
or, x=360
Therefore, the total electricity bill without the discount was Rs. 360.
Question 12.
The price of sugar has increased by 20%. Let’s work out the percentage of decrease in consumption of sugar if the monthly expenses of sugar remain same.
Answer:
Given: The percentage increment in the price of sugar=20%.
Tip:(i) if y is increased by x% then the new value of y is
(ii)
In the given question, neither the price of a single unit of sugar is written nor the quantity that is consumed daily is mentioned but the monthly cost of sugar is constant, and this is our hint and we will use this in the form of an equation.
(Actually, the price and quantity are not mentioned since percentage calculation of decrement is independent of these terms as we will see.)
Let us assume the price of a single unit of sugar be Rs. y.
Let us assume the quantity of sugar intake per month before price hike be x.
Therefore, monthly expenditure is Rs.
Now, using tip (i)
The new price of sugar is Rs. 
Let the new quantity of sugar intake per month i.e; reduced intake be z.
But, in the question, it is given that the monthly expenditure both before and after price hike should be the same.
Therefore, we can write
The new price of sugar 
Reduced intake of sugar=previous monthly
expenditure on sugar
or,
or,
Therefore, the decrement in sugar intake=x-z
Now, using tip(ii)
The decrement percentage is
=16.667%
Question 13.
When water freezes into ice, it increases in volume by 10%. Let’s work out in percentage how much it will decrease in volume if the ice melts into water.
Answer:
Given: The percentage increment in volume when water freezes to ice
=10%
Tip:(i) if y is increased by x% then the new value of y is
(ii)decrement percentage
We will try to approach this problem from backwards i.e. We will assume the volume of water that will result from melting of ice and then use the relation given in question to derive the original volume of ice that was present. After following the above steps we have obtained the volume of ice in terms of volume of water that will result due to melting of ice. Now we will subtract the volume of water from the volume of ice to obtain the decrement in volume. Then following tip(ii) we will get the required answer.
Using the theory stated above,
Let us assume the volume of water that will result due to melting of ice be x volume units.
Now according to the given relation and tip(i)
The volume of ice from which the water results is
Now the decrement in volume due to melting of ice:
Now using tip(ii)
The decrement percentage is:
(Note here the previous value = volume of ice)
=9.09%
Question 14.
Due to use of high-yielding seed Utpalbabu has got 55% production hike in paddy cultivation. But for this the cost of cultivation has increased by 40%. Previously a yield of Rs. 3000 was produced by investing Rs. 1200. Let’s work out whether his income will be increased after using high-yielding seeds.
Answer:
Given: percentage increment in production of paddy cultivation=55%
percentage increment in the cost of cultivation=40%
previous yield due to paddy cultivation= Rs. 3000
previous cost in paddy cultivation=Rs. 1200
Tip:(i) if y is increased by x% then the new value of y is
By using the data given in the question we will first figure out the previous income of Utpalbabu, then using the given tip we will figure out the new income of Utpalbabu. After getting both the incomes we will then compare the two incomes to finally get the required answer whether his income increased or decreased and by how much.
Previous Income of Utpalbabu= Yield due to cultivation-Cost due to
cultivation
=3000-1200
=Rs. 1800
Now, using tip
The new yield by using high yielding seeds
=Rs.4650
The new cost in cultivation due to high yielding seeds
=Rs.1680
Therefore, new income=New yield- New cost in cultivation
=4650-1680
=Rs.2970.
Therefore, the Increment in income for Utpalbabu
=2970-1800
=Rs.1170
Question 15.
In a legislative election, 80% voters cast their votes and the winning candidate got 65% of the cast votes. Let’s work out the percentage of total voters supported him.
Answer:
Given: Percentage of total voters that cast their votes=80%
Percentage of votes casted that were in favour of winner=65%
Tip:(i) x% of y means
(ii) To convert fraction to percentage multiple by 100.
In the question, it is said that 80% of total voters voted and out of those 80% the winner got 65% votes.
We will first assume the number of total voters as x.
Now 80% of x voted i.e.;
Now out of these voters the winner got 65% i.e.;
Therefore, fraction of voters who voted for the winner out of total eligible voters
Now, Using tip (ii)
The percentage of total eligible voters who voted for the winner is
=52%
Question 16.
This year the students of Nandlal H.S school have passed 85% in Bengali, 70% in maths and 65% in both subject scoring A+. If the number of students are 120 then let’s work out how many students
(i) got A+ in both subjects
(ii) got A+ only in maths
(iii) got A+ in Bengali
(iv) did not get A+ in both subjects
Answer:
Given: Percentage of students who got A+ in Bengali=85%
Percentage of students who got A+ in Maths=70%
Percentage of students who got A= in both subjects=65%
Total number of students =120
Tip: x% of y means
By using the given tip we can easily figure out the number of students who got A+
in subparts (i), (ii),(iii),(iv)
(i)
The no. of students who got A+ in both the subjects is
=78 students.
(ii)
The percentage of students who got A+ in Maths=70%
The percentage of students who got A+ in both subjects that is including maths and Bengali is=65%
Therefore, the percentage of students who got A+ only in Maths is=70-65
=5%
Therefore, the number of students who A+ only in Maths is 
=6 students
(iii)
The percentage of students who got A+ in Bengali is=85%
Therefore, the number of students who A+ in Bengali is
=102 students
(iv)
From the Venn Diagram drawn it is evident that the percentage of students who did not get A+ is 10%
( Percentage of students not having A+= 100%-(percentage of students
having A+ in both
subjects + percentage of
students having A+ in
only Bengali and Maths)
= 100%-90%
=10%)
Therefore, the no. of students who do not have A+ is
=
=12 students.
Question 17.
The income of Amina Bibi was increased by 20% and later decreased by 20% Let’s work out the total change of the percentage of her income.
Answer:
Given: The initial percentage increment of her salary =20%
The later percentage decrement of her salary=20%
Tip: : x% of y means .
: if y is increased by x%, then the new value of y is
: if y is decreased by x% then the new value of y is 
From the question, we see that first the salary is incremented by 20% and then later decremented by 20%. A common mistake is to say that the net change in the percentage of her salary is 0%.
The first increment of her salary by 20% is done on the initial pay of Amina Bibi.
The second decrement of her salary is done on the Increased pay of Amina Bibi, i.e.; The 20% decrement is made on the increased salary which she gets after the initial increment of her base pay.
Therefore, after stating the theory, we will implement our calculations through the given tip.
Let the initial salary of Amina Bibi be Rs. x.
Therefore, the new salary after 20% increment is 
Now, after 20% decrement on this increased salary the final salary of Amina Bibi will be
Now, the change in her pay wrt to the initial pay of Amina Bibi.
Therefore, the percentage change in her pay wrt to the initial pay of Amina Bibi.
=
=4%
Question 18.
The length of a rectangle is increased by 15% and the breadth is reduced by 15%. Let’s work out in percentage the increase or decrease of area.
Answer:
Given: The percentage increment of the length of the rectangle=15%
The percentage decrement of the breadth of the rectangle=15%
Tip: if y is increased by x% then the new value of y is
: if y is decreased by x%, then the new value of y is
Let the length of the rectangle be “L” units.
Let the breadth of the rectangle be B units
Therefore, initially before any change in the lengths of both the length and breadth of the rectangle is
=
Now, Using tip (i)
The new length of the rectangle will be:
=L
units =L
units
Now, Using tip (ii)
The new breadth of the rectangle will be:
=B
units. =B
units
Therefore, the new area of the rectangle will be:
=L
B
=LB
Therefore, the decrement in area= LB- LB
=LB
Therefore, percentage decrement in area,
=
=
=2.25%
Question 19.
The length, breadth and height of a room are 15m, 10m, 5m respectively. If the length breadth and height are increased by 10% each then work out the increase of the area of the 5 walls of the room.
Answer:
Given: The length of the room=15m
The breadth of the room =10m
The height of the room=10m
Percentage increment of the lengths=10%
Tip: if y is increased by x% then the new value of y is =y+
=y(
)
In the above diagram the walls whose area has to be calculated is shown. ( they are numbered as 1,2,3,4,5)
The total summation of these areas before any change is
= 
=300+200+150
=650
The length, breadth, height after increment will be:
length=16.5 m
breadth=11m
height=11m
Therefore, the new sum of the five areas is
=
=363+242+181.5
=786.5
Therefore, the change in the area is
=786.5-650
=136.5
Percentage change is 
= 21%
Question 20.
In annual sports, 20% of the students of took part in the 100m race. 15% of the students in 200m sprint and 10% of the students took part in the long jump event. 5% of the students took part in these three events. Let’s work out the number of students who did not take part in any of the events if the total number of students of the school were 780.
Answer:
Given: Percentage of students that took part in 100 m race=20%
Percentage of students that took part in 200m race =15%
Percentage of students that took part in long jump =10%
Percentage of students that took part in all of these events=5%
Total students=780
Tip: : x% of y means .
(Data Inadequate...
No data about percentage of students is given taking part in both 100m and 200m.
No data about percentage of students is given taking part in both 200m and long jump.
No data about percentage of students is given taking part in both 100m and long jump.)
Assuming that the above said percentages are 0 we draw a Venn diagram.
From the above Venn diagram it is clear that the percentage of students not participating in any event is 65%
(Calculation
=100%-(% of 100m only+ % of 200m only +% of long jump only +% of
all three)
=100%-(15+10+5+5)%
=65%)
Therefore, no. of students not participating
=
=507 students.