NCERT Class 7 Solutions: Integers (Chapter 1) Exercise 1.3–Part 3

Q-6 A certain freezing process requires that room temperature be lowered from 40 at the rate of 5 every hour. What will be the room temperature 10 hours after the process begins?

Solution:

Initial temperature =40

Change in temperature per hour =5

Change in temperature after 10 hours =(5)×10=50

Final Temperature =40+(50)=10

Thus, the room temperature is 10 10 hours after the process beings.

Q-7 In a class test containing 10 questions, 5 marks are awarded for every correct answer and (2) marks are awarded for every incorrect answer and 0 for questions not attempted.

  1. Mohan gets four correct and six incorrect answers. What is his score?

  2. Reshma gets five correct answers and five incorrect answers, what is her score?

  3. Heena gets two correct and five incorrect answers out of seven questions she attempts. What is her score?

Solution:

Image describing the distributive law: distributing multiplication over addition

Understanding Distributive Law

Image describing the distributive law: distributing multiplication over addition

Solution(i)

Marks given for 1 correct answer =5

Marks given for 1 wrong answer =2

Marks obtained by Mohan =marksforcorrectanswer+marksforwronganswer

=(5×4)+(2×6)

=(5×2×2)+(2×3×2)

=2(10+(6))

=2(4)

=8

Solution(ii)

Solution(iii)

Marks given for 1 correct answer =5

Marks given for 1 wrong answer =2

Marks obtained by Reshma =marksforcorrectanswer+marksforwronganswer

=(5×5)+(2×5)

=5(5+(2))

=5(3)

=15

Solution(iv)

Marks given for 1 correct answer =5

Marks given for 1 wrong answer =2

Marks obtained by Heena =marksforcorrectanswer+marksforwronganswer

=(5×2)+(2×5)

=5(2+(2))

=5(0)

=0

Q-8 A cement company earns a profit of Rs. 8 per bag of white cement sold and a loss of Rs. 5 per bag of grey cement sold.

  1. The company sells 3,000 bags of white cement and 5,000 bags of grey cement in a month. What is its profit or loss?

  2. What is the number of white cement bags it must sell to have neither profit nor loss. If the number of grey bags sold are 6,400 bags.

Solution:

Solution (a.)

Profit is denoted by a positive integer and loss is denoted by a negative integer.

Profit earned while selling 1 bag of white cement = Rs 8

Profit earned while selling 3000 bags of white cement =8×3000=24000

Loss incurred while selling 1 bag of grey cement = Rs5

Loss incurred while selling 5000 bags of grey cement =5×5000=25000

Total profit or loss earned=Profit+Loss =24000+(25000)=1000

Since this is negative a loss of Rs 1000 will be incurred by the company

Solution (b.)

Loss incurred while selling 1 bag of grey cement =Rs5

Loss incurred while selling 6400 bags of grey cement =5×6400=32000

Therefore, to make the loss no profit, total profit from white cement bags must also be 32000.

Profit earned while selling 1 bag of white cement=Rs 8

Therefore, the company must sell 320008=4000 bags.

Therefore, 4000 bags of white cement must be sold

Q-9 Replace the blank with an integer to make it a true statement.

  1. (3)×_=27

  2. 5×_=35

  3. _×(8)=56

  4. _×(12)=132

Solution:

  1. (3)×(9)_=27

  2. 5×(7)_=35

  3. 7_×(8)=56

  4. (11)_×(12)=132

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