Kerala Syllabus Class 7 Mathematics - Unit 13 Percents - Questions and Answers | Teaching Manual 

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Kerala Syllabus STD 7 Maths: Unit 13 Percents - Textbook Solutions

♦ Textbook Activities (Textbook Page No: 183)
♦ We did these problems by converting the percents into fractions. In the tables below, we give the fractional forms of some commonly used percents. Can you fill in the second table?
♦ Now try these problems:
(1) An electronics manufacturer sells some of their older models at reduced prices, as shown in the table below:
Compute the current price of each.
Answer:
Original price of the laptop = 65,000 rupees
Reduction = 10% = ¹⁰⁄₁₀₀
Reduction for 65000 rupees = 65000 X ¹⁰⁄₁₀₀ = 6500 rupees
Current price of laptop = 65000 − 6500 = 58500 rupees
Original price of the mobile phone = 25000 rupees
Reduction = 20% = ²⁰⁄₁₀₀
Reduction for 25000 rupees = 25000 X ²⁰⁄₁₀₀ = 5000 rupees
Current price of laptop = 25000 - 5000 = 20000 rupees
Original price of the smart watch = 12000 rupees
Reduction = 30% = ³⁰⁄₁₀₀
Reduction for 12000 rupees = 12000 X ³⁰⁄₁₀₀₀ = 3600 rupees
Current price of laptop = 12000 − 3600 = 8400 rupees

(2) A businessman donates 2% of his monthly profits to charity. In a certain month, he got 25000 rupees as profit. How much of this did he donate to charity?
Answer:
Profit for one month = 25000 rupees
Donation for charity = 2% of monthly profit
                              = 25000 X ²⁄₁₀₀ = 500 rupees

(3) (i) Persons earning between two and a half lakhs and five lakhs annually must pay five percent of this as income tax. How much income tax should a person with annual income three and a half lakhs pay?
Answer:
Annual income = 350000
He should pay 5% of his income as income tax.
So tax payable = 350000 X ⁵⁄₁₀₀ = 17500 rupees

(ii) Persons earning between five and ten lakhs should pay five percent of five lakhs and twenty percent of the excess over five lakhs. How much income tax should a person with annual income seven and a half lakhs pay?
Answer:
Annual income = 750000
tax payable 5% of 500000 + 20% of 250000
                  = 500000 X ⁵⁄₁₀₀ + 250000 X ²⁰⁄₁₀₀
                 = 25000 + 50000 = 75000 rupees

♦ Textbook Activities (Textbook Page No: 184)
♦ Now try these problems:
(1) Of the 50 teachers in a school, 80% are women. How many female teachers are there in the school? 
Answer:
Number of teachers = 50 
Number of female teachers = 80% of 50
         = 50 X ⁸⁰⁄₁₀₀ = 5 X 8 = 40

(2)  1450 persons voted in an election contested by two persons. The winner got 52% of the votes
(i) How many votes did he get?
(ii) By how many votes did he win?
Answer:
Number of persons voted = 1450
The winner vote percentage = 52%
The number of votes the winner got = 52% of 14500
   = 1450 X ⁵²⁄₁₀₀ = 145 X 5.2 = 754

Vote percentage of the failed candidate = 48%
Difference in percentage = 52% − 48% = 4%
So, the number of votes by which the winner won = 4% of 1450
  = 1450 X ⁴⁄₁₄₅₀ = 58

We can also do this as follows:
Number of votes obtained by the failed candidate = 1450 − 754 = 696
∴ Vote difference = 754 − 696 = 58
 
(3) 1200 kids took an exam and 65% of them got A grade. How many are they?
Answer:
Number of kids who took the examination = 1200
Number of kids who get A grade = 65% of 1200 
           = 1200 X ⁶⁵⁄₁₀₀ = 780

(4) There are 32 coconut palms in a compound. This is 50% of the total number of trees in the compound. What is the total number of trees?
Answer:
Number of coconut palms in the compound = 32
50% of the total number of trees equals the number of coconut palms.
That is ⁵⁰⁄₁₀₀ = ½ part
So, 2 times the number of coconut palms is equal to the total number of trees in the compound.
ie, total number of trees = 2 X 32 = 64

(5)  A person spends 8400 rupees a month for food. It is 25% of his monthly earnings. What is his monthly earnings?
Answer:
Food expense for one month = 8400 rupees
The person spends 25% of their monthly income on food
That is ²⁵⁄₁₀₀ = ¼ part
So, monthly income = 4 times the food expense
                = 4 X 8400 = 33600 rupees

Less and more
♦ Textbook Activities (Textbook Page No: 187)
♦ Now try these problems:
(1) A bicycle originally priced at 4000 rupees is now sold for 15% less. What is the current price?
Answer:
Price of bicycle = 4000 rupees
15% reduction means the current price is 85% of the original price.
So, current price = 85% of 4000
     = 4000 X ⁸⁵⁄₁₀₀ = 40 X 85 = 3400 rupees

(2) The monthly salary of a person was 30000 rupees last year. This year, he got an 8% raise. What is his monthly salary now?
Answer:
Monthly salary of last year = 30000 rupees
There is an increase of 8% in salary.
8% increase means 108% of last year's salary is the salary for this year.
Current salary = 108% of 30000
    = 30000 X ¹⁰⁸⁄₁₀₀ = 300 X 108 = 32400 rupees

(3) If the height and width of a rectangle are reduced by 10% each, by what percent would the area be reduced?
Answer:
Width decreasing by 10% means becoming 90%
So, new width = old width X ⁹⁰⁄₁₀₀
               = old width ⁹⁄₁₀
Height decreasing by 10% means becoming 90%
So, new height = old height X ⁹⁰⁄₁₀₀
           = old height X ⁹⁄₁₀
∴ New area = New width X New height 
         = (old width X ⁹⁄₁₀) (old height X ⁹⁄₁₀)
         = (old with X old height) X  ⁹⁄₁₀ X  ⁹⁄₁₀
         = old area X ⁸¹⁄₁₀₀ = 81% of old area.
That is area is reduced by 19%

(4)  If the height and width of a rectangle are increased by 10% each, by what percent would the area be increased?
Answer:
If the height and width of a rectangle are increased by 10% each,
New width = old width X ¹¹⁰⁄₁₀₀
New height = old height X ¹¹⁰⁄₁₀₀
New area = new width X new height
                = old width X ¹¹⁰⁄₁₀₀ X old height X ¹¹⁰⁄₁₀₀
                = (old with X old height) X ¹¹⁰⁄₁₀₀ X ¹¹⁰⁄₁₀₀
                = old area X  ¹¹⁄₁₀ X  ¹¹⁄₁₀
                = old area X ¹²¹⁄₁₀₀ = 121% of old area
So, the area is increased by 21%

Fractions and percents
♦ Textbook Activities (Textbook Page No: 188)
♦ Can you write as fractions, the parts given as percents below?
To convert a part expressed as a percent to the fractional form, ¹⁄₁₀₀ of that number is to be computed. 

To convert a part expressed as a fraction to a percent, 100 times the fraction must be computed

♦ Textbook Activities (Textbook Page No: 190)
♦ Now can’t you do these problems?
(1) In a school there are 750 students and 450 of them are girls. What is the percent of girl students?
Answer:
The number of girl students is ⁴⁵⁰⁄₇₅₀ part of the total students.
⁴⁵⁰⁄₇₅₀ = ⁴⁵⁄₇₅ = ⅗
To find the percentage, we have to multiply by 100 
⅗ X 100 = ³⁰⁰⁄₅ = 60
So, the percentage of girl students = 60%

(2) A person who earns 30000 rupees a month spends 8000 rupees on food. What percent of the earnings is this?
Answer:
The amount of money the person spends is ⁸⁰⁰⁰⁄₃₀₀₀₀ part of his earnings.
⁸⁰⁰⁰⁄₃₀₀₀₀ = ⁸⁄₃₀ = ⁴⁄₁₅
The corresponding percentage = ⁴⁄₁₅ X 100 = ⁴⁰⁰⁄₁₅ = ⁸⁰⁄₃ = 26⅔
Thus, he spends 26⅔% of his earnings on food.

(3) If a bicycle bought for 4500 rupees had to be sold for 4000 rupees, what is the loss percent?
Answer:
Loss = 4500 − 4000 = 500 rupees
That is ⁵⁰⁰⁄₄₅₀₀ = ⅑ part of the price for which it was bought.
Thus the corresponding percentage = ⅑ X 100 = ¹⁰⁰⁄₉ = 11⅑
So, the percentage of loss = 11⅑%

(4) 1600 persons voted in an election and the winner got 900 votes. What percent of the total votes is this?
Answer:
The votes for the winning candidate are ⁹⁰⁰⁄₁₆₀₀ part of the total votes polled.
⁹⁰⁰⁄₁₆₀₀ = ⁹⁄₁₆ part.
To find the percentage, we have to multiply it by 100
⁹⁄₁₆ X 100 = ⁹⁰⁰⁄₁₆ = ²²⁵⁄₄ = 56¼
That is, the winner got 56¼% of the votes.

(5) Ajayan’s salary is 25% more than Sajayan’s salary. By what percent of Ajayan’s salary is Sajayan’s salary less?
Answer:
Ajayan’s salary is 25% more than Sajayan’s salary means ²⁵⁄₁₀₀ = ¼ part is more than Sajayan's salary.
If we take the salary of Sajayan as 's'
¼th of Sajayan's salary = s X ¼ = ˢ⁄₄
Then Ajayan’s salary = s + s¼ = s (1+ ¼) = s (⁵⁄₄)
That is, Ajayan’s salary is ⁵⁄₄ times Sajayan's salary.
Conversely,
Sajayan's salary is ⅘ part of Ajayan’s salary.
If we convert ⅘ into percent, ⅘ X 100 = 80
So, Sajayan's salary is 80% of Ajayan’s salary.
That is Sajayan's salary is 20% less than Ajayan’s salary.