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Kerala State Syllabus 6th Standard Maths Solutions Chapter 9 How Much of Hundred?
How Much of Hundred? Text Book Questions and Answers
Sale Textbook Page No. 135
See the ad?
The table shows the original price of some of the things in this shop. We want to calculate the new prices: How?
It’s 10 rupees less for every 100 rupees. So to compute the reduction in price, we must first find out how many 100’s are there in the original price and then multiply it by 10.
For example , the original price of a fan is 1200 rupees.
That is 12 hundreds: so the reduction in price is
12 × 10 = 120 rupees
We can do both operations together:
\(\frac{1200}{100}\) × 10 = 120
So the price of a fan now is 1200 – 120 = 1080 rupees.
Similarly, can’t you compute the prices of others now?
Answer:
Clock = 450 rupees
Iron = 720 rupees
CFL Bulb = 225 rupees
Mixer = 2250 rupees
Cooker = 1260 rupees
Explanation:
Clock :
the original price of a clock is 500 rupees.
It’s 10 rupees less for every 100 rupees.
That is 5 hundreds: so the reduction in price is
5 × 10 = 50 rupees
We can do both operations together:
\(\frac{500}{100}\) × 10 = 50
So the price of a clock now is 500 – 50 = 450 rupees.
Iron :
the original price of a Iron is 800 rupees.
It’s 10 rupees less for every 100 rupees.
That is 8 hundreds: so the reduction in price is
8 × 10 = 80 rupees
We can do both operations together:
\(\frac{800}{100}\) × 10 = 80
So the price of a iron now is 800 – 80 = 720 rupees.
CFL Bulb :
the original price of a CF Bulb is 250 rupees.
It’s 10 rupees less for every 100 rupees.
That is 2 hundred and 50 fifty rupees
so the reduction in price is
2.5 × 10 = 25 rupees
We can do both operations together:
\(\frac{250}{100}\) × 10 = 25
So the price of a CF Bulb now is 250 – 25 = 225 rupees.
Cooker :
the original price of a cooker is 1400 rupees.
It’s 10 rupees less for every 100 rupees.
That is 14 hundreds: so the reduction in price is
14 × 10 = 140 rupees
We can do both operations together:
\(\frac{1400}{100}\) × 10 = 140
So the price of a cooker now is 1400 – 140 = 1260 rupees.
Mixer :
the original price of a mixer is 2500 rupees.
It’s 10 rupees less for every 100 rupees.
That is 25 hundreds: so the reduction in price is
25 × 10 = 250 rupees
We can do both operations together:
\(\frac{2500}{100}\) × 10 = 250
So the price of a mixer now is 2500 – 250 = 2250 rupees.
Loans
A co-operative bank offers agricultural loans. It must be paid back in one year; and for every hundred rupees, 12 rupees more should be given.
See the amounts of loan some people have taken out:
Calculate how much each should pay back.
To know how much more each should give back, we must find out how many hundreds are there in the loan and multiply it by 12.
As before, we need only divide by 100 and multiply by 12.
For example, Raji’s loan is 1550 rupees.
To calculate how much more she has to pay back, we divide 1550 by 100 and multiply by 12:
\(\frac{1550}{100}\) × 12 = 186
So, Raji has to pay back 1550 + 186 = 1736 rupees.
Like this, calculate how much each has to pay back.
To know how much more each should give back,
we must find out how many hundreds are there in the loan and multiply it by 12.
As before, we need only divide by 100 and multiply by 12.
Sabu’s loan is 4000 rupees.
To calculate how much more she has to pay back, we divide 4000 by 100 and multiply by 12:
\(\frac{4000}{100}\) × 12 = 480
So, Sabu has to pay back 4000 + 480 = 4480 rupees.
Suma’s loan is 5500 rupees.
To calculate how much more she has to pay back, we divide 5500 by 100 and multiply by 12:
\(\frac{5500}{100}\) × 12 = 660
So, Suma has to pay back 5500 + 660 = 6160 rupees.
Gokul’s loan is 3750 rupees.
To calculate how much more she has to pay back, we divide 3750 by 100 and multiply by 12:
\(\frac{3750}{100}\) × 12 = 450
So, Gokul has to pay back 3750 + 450 = 4200 rupees.
Nabeel’s loan is 3800 rupees.
To calculate how much more she has to pay back, we divide 3750 by 100 and multiply by 12:
\(\frac{3800}{100}\) × 12 = 456
So, Nabeel has to pay back 3800 + 456 = 4256 rupees.
Percent
In the first problem. the reduction in price is 10 rupees for each hundred rupees.
We say that there is 10 percent reduction in price.
10 percent is written as 10%.
In the loan problem, 12 rupees more for every hundred rupees should be paid back.
That is, 12%( 12 percent) more should be paid back.
The word per means for each. The cent part comes from the Latin word centum meaning hundred.
Donations Textbook Page No. 137
Each month Joseph donates 8% of his earnings to the Medical Aid Fund. He earned 12000 rupees in January. How much should he donate that month?
8 percent means ,8 for each hundred. So we must find out the number of hundreds in 12000 and multiply it by 8:
\(\frac{12000}{100}\) × 8 = 120 × 8 = 960
So, Joseph would donate 960 rupees that month.
This can also be calculated as 12000 × \(\frac{8}{100}\).
That is, \(\frac{8}{100}\) of 12000.
Joseph’s friend Ah donates 12% of his monthly earnings. In January he earned 15000 rupees. How much would he give.
We can think of 12% as 12 for each hundred and calculate
\(\frac{15000}{100}\) × 12
Or we can think of 12% as \(\frac{12}{100}\) and calculate.
15000 × \(\frac{12}{100}\)
Do it any way you like.
Answer:
18,000
Explanation:
Joseph’s friend Ah donates 12% of his monthly earnings.
In January he earned 15000 rupees.
Total amount he gave = \(\frac{15000}{100}\) × 12
= 150 x 12 = 18,000
Or we can think of 12% as \(\frac{12}{100}\)
15000 × \(\frac{12}{100}\)
= \(\frac{1,800,000}{100}\)
= 18,000
Textbook Page No. 138
Question 1.
See the ad.
Sheela bought cloths worth 1800 rupees. How much should she pay?
Answer:
1260 rupees,
Explanation:
30 percent means ,30 for each hundred.
So we must find out the number of hundreds in 1800 and multiply it by 30:
Sheela bought cloths worth 1800 rupees
\(\frac{1800}{100}\) × 30 = 18 x 30 = 540
So, Sheela amount to be paid after discount is
1800 – 540 = 1260 rupees
Question 2.
Johny save 15% of his earnings each month. In January he got 32000 rupees. How much would he save?
Answer:
4800 rupees,
Explanation:
Johny save 15% of his earnings each month, in January he got 32000 rupees.
15 percent means ,15 for each hundred.
So we must find out the number of hundreds in 32000 and multiply it by 15:
\(\frac{32000}{100}\) × 15 = 320 x 15 = 4800 rupees
Question 3.
A TV manufacturer decides to raise prices by 5% next month. The price of a model is 26000 rupees now. What would be its price next month?
Answer:
27300 rupees,
Explanation:
A TV manufacturer decides to raise prices by 5% next month.
The price of a model is 26000 rupees now.
5 percent means ,5 for each hundred.
So we must find out the number of hundreds in 26000 and multiply it by 5:
\(\frac{26000}{100}\) × 5 = 260 x 5 = 1300 rupees
A TV manufacturer decides to raise prices by 5% next month = 1300 rupees
The TV price in the next month is,
26000 + 1300 = 27300 rupees
Question 4.
A car manufacturer decides to lower prices by 2% from next month. What would be the price next month for a car, now priced at 250000 rupees?
Answer:
245000 rupees
Explanation:
A car manufacturer decides to lower prices by 2% next month.
The price of a model is 250000 rupees now.
2 percent means ,2 for each hundred.
So we must find out the number of hundreds in 250000 and multiply it by 2:
\(\frac{250000}{100}\) × 2 = 2500 x 2 = 5000 rupees
A car manufacturer decides to lower prices by 2% next month = 5000 rupees
The car price in the next month is,
250000 – 5000 = 245000 rupees
Question 5.
A company pays 8% of a month’s salary as festival allowance. How much festival allowance would a person whose salary is 12875 rupees get?
Answer:
13905 rupees
Explanation:
A company pays 8% of a month’s salary as festival allowance.
The price of a model is 12875 rupees now.
8 percent means ,8 for each hundred.
So we must find out the number of hundreds in 12875 and multiply it by 8:
\(\frac{12875}{100}\) × 8 = 128.75 x 8 = 1030 rupees
festival allowance would a person whose salary is 12875 rupees get is,
12875 + 1030 = 13905 rupees
Another percent
In a school, 240 children took an exam and 40% of them got A grade in all subjects.
What does it mean?
There is no sense in saying that 40 children out of every 100 got A grade.
Here it means, \(\frac{40}{100}\) of the total number of children got A grades in all subjects.
That is, the number of children who got A grade is
240 × \(\frac{40}{100}\) = 96
What is 20% of 60%? What about 60% of 20. Are 40% of 30 and 30% of 40 equal?
Answer:
Yes, 40% of 30 and 30% of 40 equal.
Explanation:
20% of 60%
(20 x 60)% = \(\frac{20 x 60}{100}\) = 12
60% of 20
20 × \(\frac{60}{100}\) = 12
40% of 30
30 × \(\frac{40}{100}\) = 12
Let’s look at another problem:
There are 40 children in a class and 50% of them are boys. How many boys are there in this class?
50% of the class are boys means, \(\frac{50}{100}\) of the total number of children in the class are boys.
That is, \(\frac{1}{2}\) of the total number, or half the total.
So there are 20 boys in the class.
Election
There are 1200 voters in a panchayat ward and 80% of them voted in an election. How many people voted’?
The number of persons who voted is \(\frac{80}{100}\) of the total number of voters.
So the number of persons voted is \(\frac{80}{100}\) of 1200.
That is, 1200 × \(\frac{80}{100}\) = 960
Textbook Page No. 140
Question 1.
In a company, 46% of the workers are women. It has 300 workers in all. How many of them are women?
Answer:
138 are women.
Explanation:
The number of workers in a company are 300,
46% of the workers are women.
300 x \(\frac{46}{100}\) = 138
Question 2.
In a class, 20% of the children are members of the Math Club. There are 35 children in the class. How many are members of the Math Club?
Answer:
7 member are in the Math Club.
Explanation:
In a class, 20% of the children are members of the Math Club.
20 percent means ,20 for each hundred.
So we must find out the number of hundreds in 1450 and multiply it by 54
35 x \(\frac{20}{100}\) = 7
Question 3.
In an election, the candidate who won got 54% of the votes. 1450 votes were polled. How many votes did the winner get?
Answer:
783 votes.
Explanation:
54 percent means ,54 for each hundred.
So we must find out the number of hundreds in 1450 and multiply it by 54
In an election, 54% the candidate who won got 54% of the votes
1450 x \(\frac{54}{100}\) = 783
Question 4.
The price of a car is 530000 rupees now. The manufacturer decides to reduce the price by 2% next month. What would be the reduction in price? What would be the new price?
Answer:
519400 rupees.
Explanation:
2 percent means ,2 for each hundred.
So we must find out the number of hundreds in 530000 and multiply it by 2
The price of a car is 530000 rupees now.
The manufacturer decides to reduce the price by 2% next month.
530000 x \(\frac{2}{100}\) = 10600
530000 – 10600 = 519400
Question 5.
1300 children took the Nu MATS test and 65%of them scored more than 25. How many are they?
Answer:
845 children scored more then 25.
Explanation:
65 percent means ,65 for each hundred.
So we must find out the number of hundreds in 1300 and multiply it by 13
1300 x \(\frac{65}{100}\) = 845
845 children scored more then 25
The other percent
60% of the workers in a company are women.
What all things do we know from this statement?
\(\frac{60}{100}\) of the total number of workers are women.
So what fraction of the workers are men? \(\frac{40}{100}\), right?
That is 40% of the workers are men.
In other words, \(\frac{3}{5}\) of the workers are women and \(\frac{2}{5}\) of the workers are men (How come?)
There were 320 children in the sub-district camp for scout and guides. 55% of them were guides and the rest, scout. How many scouts were there?
The percent of scouts is 1oo – 55 = 45.
So the number of scouts is 320 × \(\frac{45}{100}\)
This is easy to calculate, isn’t it?
Answer:
Yes,
Explanation:
The percent of scouts is 1oo – 55 = 45.
So the number of scouts is
320 × \(\frac{45}{100}\) = 144
Textbook Page No. 141
Question 1.
Of the 420 children in a school, 5% did not come one day. How many came to school that day?
Answer:
399 children came to school.
Explanation:
5 percent means ,5 for each hundred.
So we must find out the number of hundreds in 4.20 and multiply it by 5.
420 x \(\frac{5}{100}\) = 21
420 – 21 = 399
Question 2.
There are 280 plants in Sabu’s garden 70% of them are flowering. How many are non flowering?
Answer:
84 plants are non flowering.
Explanation:
70 percent means ,70 for each hundred.
So we must find out the number of hundreds in 2.80 and multiply it by 70.
280 x \(\frac{70}{100}\) = 196
280 – 196 = 84
Question 3.
There are 480 vehicles in a parking lot. Of these, 45% are motorbikes and 4% are cars. The rest are mini buses. How many mini buses are there?
Answer:
245 mini buses.
Explanation:
45% + 4% = 49%
100% – 49% = 51%
51% vehicles are mini buses.
480 x \(\frac{51}{100}\) = 244.8
So, there are 245 mini buses.
How many in all?
In a compound, there are 32 coconut trees and they form 50% of the total number of trees.
How many trees are there in all?
50% of the trees means \(\frac{50}{100}\) = \(\frac{1}{2}\) of the trees.
Thus, half the trees are coconut palms and so the total number of trees is double the number of coconut palms.
That is the total number of trees = 2 × 32 = 64.
In the sub-district Math fair, 60% of the children were girls. The actual number of girls was 108. How many children were there in all?
The number of girls is \(\frac{60}{100}\) = \(\frac{3}{5}\) of the total.
This means \(\frac{3}{5}\) of the total number is 108.
So the total number is \(\frac{5}{3}\) times 108.
That is, 108 × \(\frac{5}{3}\) = 180.
Thus we see that 180 children were there at the math fair.
Textbook Page No. 142
Question 1.
26 children of a class got A grade in an exam. It is 65% of the total number in the class. How many are there in the class?
Answer:
40 children.
Explanation:
26 children of a class got A grade in an exam.
It is 65% of the total number in the class means \(\frac{65}{100}\)x = 26
Total number of children in the class
x = \(\frac{100}{65}\) x 26
x = 26 \(\frac{20}{13}\)
x = 40
Question 2.
Jayan spent 8400 rupees in a month for food and it is 35% of his earnings. How much did he earn that month?
Answer:
24,000 rupees.
Explanation:
Jayan spent 8400 rupees in a month for food and it is 35% of his earnings.
Monthly amount earned by Jayan be x.
35% of x = 8400
\(\frac{35}{100}\)x = 8400
x = 8400\(\frac{20}{7}\)
x = 24000.
Question 3.
32 teachers of a school are male and they form 40% of the total number of teachers. How many teachers are there in the school?
Answer:
80 teachers.
Explanation:
Let the total number of teachers = x
Number of male teachers = 32
40% of the total no. of teachers = male teachers.
40% of x = 32
\(\frac{40}{100}\)x = 32
\(\frac{2}{5}\)x = 32
x = 32\(\frac{5}{2}\)
x = \(\frac{160}{2}\)
x = 80
Percent of percent
A man spends 20% of his earnings on education and 25% of this amount on books. What percent of his total earnings does he spend on books’?
It is \(\frac{25}{100}\) of \(\frac{20}{100}\) of the total earnings.
\(\frac{25}{100}\) of \(\frac{25}{100}\) means
= \(\frac{20}{100}\) × \(\frac{25}{100}\)
= \(\frac{1}{5}\) \(\frac{25}{100}\) = \(\frac{5}{100}\)
Thus the amount spend on books is 5% of the total earnings.
Now what percent of a number is 40% of its 30% percent’?
Answer:
12% of a number is 40% of its 30% percent.
Explanation:
It is \(\frac{40}{100}\) of \(\frac{30}{100}\) of the total earnings.
\(\frac{40}{100}\) of \(\frac{30}{100}\) means
= \(\frac{30}{100}\) × \(\frac{40}{100}\)
= \(\frac{3}{10}\) \(\frac{2}{5}\)
= \(\frac{3}{25}\) x 100
= \(\frac{300}{25}\)
= 12
Thus the amount spend on books is 12% of the total earnings.
Changing percent
A shop offers 20% reduction in prices. Ravi bought a shirt worth 400 rupees from this shop. How much should he pay?
He need only pay \(\frac{20}{100}\) of 400 less.
400 × \(\frac{20}{100}\) = 80
So, he must pay
400 – 80 = 320 rupees.
There is another way to do this.
The reduction in price is 20% of 400.
So he needs to pay only 80% of 400
80% of 400 = 400 × \(\frac{80}{100}\) = 320 rupees.
Now look at another problem:
In a school, there were 800 children last year and this year, the number is 12% more. How many children are there now?
The increase is 800 × \(\frac{12}{100}\) = 96
So then we can calculate the number of children now.
This we can do in a different way.
800 + (800 × \(\frac{12}{100}\)) = 800 × (1 + \(\frac{12}{100}\))
= 800 × \(\frac{112}{100}\) = 896
We can say \(\frac{112}{100}\) times is 112 percent(112%).
Area
If the length and breadth of a rectangle are increased by 10%, by how much percent would the area increase? What if length is increased by 10% and the breadth decreased by 10%?
Answer:
If the length and breadth of a rectangle are increased by 10%,
Area = 21%
If length is increased by 10% and the breadth decreased by 10%,
Area = 1%
Explanation:
Let length = 100; Breadth = 100
Area = 100 x 100 = 10000
After increasing length and breadth 10%
length = 110; Breadth = 110
Area = 110 x 110 = 12100
Increase in Area = 12100 – 10000 = 2100
% increase in area = \(\frac{2100}{10000}\) x 100 = 21%
if length is increased by 10% and the breadth decreased by 10%
length = 110; Breadth = 90
Area = 110 x 90 = 9900
% increase in area = \(\frac{9900}{100}\) = 99%
% of change in new area = 100 – 99 = 1%
Textbook Page No. 143
Question 1.
The price of a bicycle was 3400 rupees last month. Now it is reduced by 15%. What is the price now?
Answer:
2,890 rupees.
Explanation:
Cost of bicycle = 3400 rupees last month.
,Now it is reduced by 15%.
Total price = \(\frac{15}{100}\) x 3400
= 15 x 34
= 510 rupees.
Cost of bicycle now = Cost of bicycle last month – Amount reduced.
= 3400 – 510 = 2890
Question 2.
A watch priced at 3680 rupees is now sold for 20% less. What is the price now?
Answer:
2,944 rupees.
Explanation:
Initial cost of watch = 3680 rupees.
sold for 20% less.
Amount reduced = 3680 x \(\frac{20}{100}\)
= 2 x 368 = 736
Price of watch now = Initial price – Amount reduced.
= 3680 – 736
= 2944 rupees.
Question 3.
The amount of rainfall this year is calculated to be 20% more than last year. Last year’s rainfall was 230 centimeters. What is the amount of rainfall this year?
Answer:
276 cm.
Explanation:
The amount of rainfall this year is calculated to be 20% more than last year.
Last year’s rainfall was 230 centimeters.
Amount increases in rainfall = 20% of 230 cm
= \(\frac{20}{100}\) x 230
= 46 cm
Total amount of rainfall this year = last year rainfall + increase of rainfall this year.
= 230 + 46
= 276 cm
Question 4.
A person earned 12000 rupees last month and it is 6% more this month. How much is this month’s earning?
Answer:
12,720 rupees.
Explanation:
Amount earned last month = 12000 rupees.
Increase 6% more in this month.
Increased amount = 6% of 12000 rupees.
= \(\frac{6}{100}\) x 12000
= 720 rupees.
Amount earned this month = Amount earned last month + Incresed amount
= 12000 + 720
= 12720 rupees.
Fractional percent
We have said that 25% of something means \(\frac{25}{100}\) of that number;
which means \(\frac{1}{4}\) of that.
What about 125% of something’?
\(\frac{125}{100}\) times it; or 1\(\frac{1}{4}\) of it.
Thus percent of something means a fraction of it or certain times it.
We can put it in a different manner:
10% means 10 times \(\frac{1}{100}\)
20% means 20 times \(\frac{1}{100}\)
25% means 25 times \(\frac{1}{100}\)
60% means 60 times \(\frac{1}{100}\)
In this manner, 12\(\frac{1}{2}\) times of \(\frac{1}{100}\) can be said to be 12\(\frac{1}{2}\) %
What fraction is this?
\(\frac{1}{100}\) × 12\(\frac{1}{2}\) = \(\frac{1}{100}\) × \(\frac{25}{2}\) = \(\frac{1}{8}\)
Thus, 12\(\frac{1}{2}\) % of something means \(\frac{1}{8}\) of that.
12\(\frac{1}{2}\) % can also be written 12.5%
So, what does 33\(\frac{1}{3}\) % mean?
33\(\frac{1}{3}\) of \(\frac{1}{100}\).
\(\frac{1}{100}\) × 33\(\frac{1}{3}\) = \(\frac{1}{100}\) × \(\frac{100}{3}\) = \(\frac{1}{3}\)
So, 33\(\frac{1}{3}\)% of something means \(\frac{1}{3}\) of that.
Textbook Page No. 144
Question 1.
Explain each percent below as a fraction of something.
i) 6\(\frac{1}{4}\)%
Answer:
\(\frac{1}{16}\) of that or 6.25%.
Explanation:
6\(\frac{1}{4}\) of \(\frac{1}{100}\).
\(\frac{25}{4}\) × \(\frac{1}{100}\)
= \(\frac{25}{400}\)
= \(\frac{1}{16}\)
=6.25%
So, 6\(\frac{1}{4}\)% of something means \(\frac{1}{16}\) of that or 6.25%.
ii) 6\(\frac{2}{3}\)%
Answer:
\(\frac{1}{15}\) of that or 6.67%.
Explanation:
6\(\frac{2}{3}\) of \(\frac{1}{100}\).
\(\frac{20}{3}\) × \(\frac{1}{100}\)
= \(\frac{20}{300}\)
= \(\frac{2}{30}\)
= \(\frac{1}{15}\)
= 6.67%
So, 6\(\frac{2}{3}\)% of something means \(\frac{1}{15}\) of that or 6.67%.
iii) 8\(\frac{1}{3}\)%
Answer:
\(\frac{1}{1200}\) of that or 0.0012%.
Explanation:
8\(\frac{1}{3}\) of \(\frac{1}{100}\).
\(\frac{25}{3}\) × \(\frac{1}{100}\)
= \(\frac{25}{300}\)
= \(\frac{1}{12}\)
= 8.33%
So, 8\(\frac{1}{3}\)% of something means \(\frac{1}{12}\) of that or 8.33%.
iv) 16\(\frac{2}{3}\)%
Answer:
\(\frac{5}{30}\) of that or 16.6%.
Explanation:
16\(\frac{2}{3}\) of \(\frac{1}{100}\).
\(\frac{50}{3}\) × \(\frac{1}{100}\)
= \(\frac{50}{300}\)
= \(\frac{5}{30}\)
= 16.6%
So, 16\(\frac{2}{3}\)% of something means \(\frac{5}{30}\) of that or 16.6%.
v) 62\(\frac{1}{2}\)%
Answer:
\(\frac{31}{50}\) of that or 62%.
Explanation:
62\(\frac{1}{2}\) of \(\frac{1}{100}\).
\(\frac{124}{2}\) × \(\frac{1}{100}\)
= \(\frac{3131}{50}\)
= 62%
So, 62\(\frac{1}{2}\)% of something means \(\frac{124}{200}\) of that or 62%.
vi) 66\(\frac{2}{3}\)%
Answer:
\(\frac{2}{3}\) of that or 66.6%.
Explanation:
66\(\frac{2}{3}\) of \(\frac{1}{100}\).
\(\frac{200}{3}\) × \(\frac{1}{100}\)
= \(\frac{200}{300}\)
= \(\frac{2}{3}\)
= 66.6%
So, 66\(\frac{2}{3}\)% of something means \(\frac{2}{3}\) of that or 66.6%.
vii) 83\(\frac{1}{3}\)%
Answer:
\(\frac{5}{6}\) of that or 83.3%.
Explanation:
83\(\frac{1}{3}\) of \(\frac{1}{100}\).
\(\frac{250}{3}\) × \(\frac{1}{100}\)
= \(\frac{250}{300}\)
= \(\frac{25}{30}\)
= \(\frac{5}{6}\)
= 83.3%
So, 83\(\frac{1}{3}\)% of something means \(\frac{5}{6}\) of that or 83.3%.
Fraction and percent
We have seen that any percent can be explained as a fraction. On the other hand, can we express every fraction of something as a percent?
For that, we look at percents in a different way.
For example,
10% means 10 times \(\frac{1}{100}\).
We can put it differently;
10% means of 10 times \(\frac{1}{100}\)
Similarly, we can say
20% means \(\frac{1}{100}\) of 20 times.
25% means \(\frac{1}{100}\) of 25 times.
12\(\frac{1}{2}\) % means of 12\(\frac{1}{2}\) times.
That is the fraction expressing a percent as a part or times of something is \(\frac{1}{100}\) of the number given as a percent.
So the percent number is 100 times this fraction.
For example, let’s compute what percent of something, \(\frac{2}{5}\) of it gives.
\(\frac{2}{5}\) is \(\frac{1}{100}\) of the percent number.
So, the percent number is 100 times \(\frac{2}{5}\)
\(\frac{2}{5}\) × 100 = 40
Thus, \(\frac{2}{5}\) of something is 40% of it.
Now look at this problem:
In a school, 120 children appeared for SSLC examination. 110 children qualified for higher studies. What part of the children appeared for examination qualified?
\(\frac{110}{120}\) = \(\frac{11}{25}\)
That is, this fraction is the \(\frac{1}{100}\) parts of the percent of children qualified. Then percent of qualified children is 100 times of this. That is,
\(\frac{11}{25}\) × 100 = 91\(\frac{2}{3}\)
Therefore, 91\(\frac{2}{3}\)% of children is qualified for higher studies.
Question 1.
There are 750 children in a school and 450 of them are girls. What is the percent of girls?
Answer:
60%
Explanation:
There are 750 children in a school.
450 of them are girls.
The percent of girls = \(\frac{450}{750}\) × 100
= \(\frac{9}{15}\) × 100
= \(\frac{900}{15}\)
= 60%
Question 2.
Rafi earns 20000 rupees a month and he spends 6400 rupees from this on food. What percent of his earnings is this?
Answer:
percent of his earnings is 32 or 32%
Explanation:
Rafi monthly earnings = 20000 rupees.
Rafi spent on food = 6400 rupees.
% of his earnings = (Amount spent on food ÷ Rafi monthly earnings) x 100
= \(\frac{6400}{20000}\) x 100
= \(\frac{64}{200}\) x 100
= 32%
Question 3.
Jameel’s salary was 20000 rupees last month and 21000 rupees this month. By what percent has the salary increased?
Answer:
Salary increase 5%
Explanation:
Jameel’s last month salary = 20000 rupees.
Jameel’s this month salary = 21000 rupees.
Increase in salary = 21000 – 20000 = 1000 rupees
percent of increased salary = \(\frac{1000}{20000}\) x 100
= \(\frac{10}{2}\)
= 5%
Question 4.
Of 600 grams of sugar, 500 grams is used up. What percent is left?
Answer:
16.6% or 17%
Explanation:
Total grams of sugar = 600gm
Used sugar = 500 gm
Sugar left = 600 – 500 = 100 gm
% of sugar left = \(\frac{100}{600}\) x 100
= \(\frac{100}{6}\)
= \(\frac{50}{3}\)
= 16.6% or 17%
Question 5.
The sides of a square are increased by 10% to make a larger square. By what percent is the area increased?
Answer:
21% of area is increased.
Explanation:
Let the side of the smaller square is x cm.
Area of smaller square is (x cm)2.
Side of the larger square is increased by 10%
Side is increased by 10% of x.
= \(\frac{10}{100}\)x
= \(\frac{x}{10}\)cm
Side of larger square = x + \(\frac{x}{10}\)
= \(\frac{11x}{10}\)
Area of larger square = (\(\frac{11x}{10}\))2
= (\(\frac{121x}{100}\))2
Increased area = Area of larger square – area of smaller square
= \(\frac{21}{100}\)x2 cm2
Percentage of increased area = (Increased area ÷ Area of the smaller square) x 100
= (\(\frac{21}{100}\)x2 cm2÷ x2 cm2) x 100
= \(\frac{21}{100}\) x 100
= 21%
Question 6.
Ajayan’s salary is 25% more than Vijayan’s salary. By what percent of Ajayan’s salary is Vijayan’s salary less’?
Answer:
20% less than Ajayan’s salary.
Explanation:
Let Vijayan’s salary be 100
Ajayan’s salary = \(\frac{125}{100}\) x 100
= 125
Vijayan’s salary is \(\frac{100 X 100}{125}\) % of Ajayan’s salary.
= 80% of Ajayan’s salary.
Vijayan’s salary = 100 – 80 = 20% less than Ajayan’s
Textbook Page No. 147
Question 1.
Express the percent each fraction below indicates.
i) \(\frac{3}{8}\)
Answer:
37.5%
Explanation:
\(\frac{3}{8}\) x 100
= \(\frac{3x 100}{8}\)
= 37.5 %
ii) \(\frac{7}{20}\)
Answer:
15%
Explanation:
\(\frac{3}{20}\) x 100
= \(\frac{3x 100}{20}\)
= 15 %
iii) \(\frac{2}{3}\)
Answer:
66.67%
Explanation:
\(\frac{2}{3}\) x 100
= \(\frac{2 x 100}{3}\)
= 66.67%
iv) \(\frac{28}{25}\)
Answer:
112%
Explanation:
\(\frac{28}{25\) x 100
= \(\frac{28 x 100}{25}\)
= 112%
v) 2\(\frac{1}{3}\)
Answer:
33.34%
Explanation:
\(\frac{1}{3}\) x 100
= \(\frac{1 x 100}{3}\)
= 33.34%
Question 2.
What is the difference between 40% of 60 and 60% of 40?
Answer:
Both are same 24%
Explanation:
40% of 60
\(\frac{40}{100}\) x 60
= \(\frac{40 x 60}{100}\)
= 24
60% of 40
\(\frac{60}{100}\) x 40
= \(\frac{60 x 40}{100}\)
= 24
the difference between 40% of 60 and 60% of 40 are same.
Question 3.
In a school there are 1240 children and 30% of them are girls. How many boys are there in the school?
Answer:
372 boys.
Explanation:
In a school there are 1240 children,
30% of them are girls.
Total boys in the school = \(\frac{30}{100}\) x 1240
= \(\frac{1240 x 30}{100}\)
= 124 x 3
= 372 boys.
Question 4.
If 40% of 20 is added to 30% of 50, we get 50% of a number. What is this number?
Answer:
46
Explanation:
If 40% of 20 is added to 30% of 50,
we get 50% of a number
\(\frac{40}{100}\) x 20
= \(\frac{40 x 20}{100}\)
= 8
\(\frac{30}{100}\) x 50
= \(\frac{30 x 50}{100}\)
= 15
= 8+15 = 23
50% of a number is 23
100 % is 2 x 23 = 46
Question 5.
23 percent of a number is 69. What is the number?
Answer:
300
Explanation:
23 percent of a number is 69
x . \(\frac{23}{100}\) = 69
23 x = 69 x 100
x = \(\frac{69 x 100}{23}\)
x = 300
Question 6.
10 percent of a number is 1.5. What is the number?
Answer:
300
Explanation:
10 percent of a number is 1.5.
x . \(\frac{10}{100}\) = 1.5
23 x = 69 x 100
x = \(\frac{69 x 100}{23}\)
x = 300
Question 7.
The price of an article was 1800 rupees last month. The price is reduced by 10% this month .The shopkeeper says this price would be increased by 10% next month. What would be the price next month?
Answer:
1782 rupees.
Explanation:
The price of an article was 1800 rupees last month.
The price is reduced by 10% this month.
Amount reduced = \(\frac{10}{100}\) x 1800 = 180
Cost of article this month = 1800 – 180 = 1620
The shopkeeper says this price would be increased by 10% next month.
The price for next month = \(\frac{10}{100}\) x 1620 = 162
Cost of article for next month = cost of article this month + amount increased
= 1620 + 162 = 1782
Question 8.
Kannan has 600 rupees. He gave 50% of this to Thomas. Thomas gave 33\(\frac{1}{3}\) % of what he got to Hamza. How much did Hamza get?
Answer:
Hamza get 100 rupees.
Explanation:
Money Kannan has = 600 rupees
He gave 50% of this to Thomas.
Amount of money Kannan gives to Thomas = \(\frac{50}{100}\) x 600 = 300
Now Thomas has 300 rupees.
Thomas gave 3\(\frac{1}{3}\) % of what he got to Hamza.
% of money Thomas given to Hamza = 33\(\frac{1}{3}\)%
Amount of money Thomas given to Hamza = 33\(\frac{1}{3}\)% x 300
= \(\frac{100}{3}\) x \(\frac{1}{100}\) x 300
= 100
Question 9.
All children in class 7 passed the math exam. Details of grades are given below.
Fill in the blanks.
Answer:
Explanation:
As we know total percentage is 100%
40 + 30 + 25 + x = 100
95 + x = 100
x = 100 – 95
x = 5%
Number of children in Grade D
5% = 9
25% = x
by cross multiplying the above two
Number of children in Grade C
x 5% = 9 x 25%
x = \(\frac{9 × 25}{5}\)
x = 45
Number of children in Grade B
x 25% = 45 x 30%
x = \(\frac{45 × 30}{25}\)
x = 54
Number of children in Grade A
x 30% = 54 x 40%
x = \(\frac{54 × 40}{30}\)
x = 72