NCERT Solutions Class 7th Maths Chapter – 1 Integers All Example

Example. 1 Write down a pair of integers whose

(a) sum is -3
(b) difference is -5
(c) difference is 2
(d) sum is 0

Solution –

(a) (-1)+(-2) = -3 or (-5) + 2 = -3
(b) (-9)-(-4) = -5 or (-2)-3 = -5
(c) (-7)-(-9) = 2 or 1-(-1) = 2
(d) (-10)+10 = 0 or 5+(-5) = 0

Can you write more pairs in these examples?

Example. 2 In a test (+5) marks are given for every correct answer and (-2) marks are given for every incorrect answer.

(i) Radhika answered all the questions and scored 30 marks though she got 10 correct answers.

(ii) Jay also answered all the questions and scored (-12) marks though he got 4 correct answers. How many incorrect answers had they attempted?

Solution –

(i) Marks given for one correct answer=5
So, marks given for 10 correct answers = 5 x 10 = 50
Radhika’s score = 30
Marks obtained for incorrect answers = 30-50 = -20
Marks given for one incorrect answer = (-2)
Therefore, number of incorrect answers = (-20)÷(-2) = 10

(ii) Marks given for 4 correct answers = 5×4 = 20
Jay’s score = -12
Marks obtained for incorrect answers =-12-20 = -32
Marks given for one incorrect answer = (-2)
Therefore number of incorrect answers = (-32)÷(-2) = 16

Example. 3 A shopkeeper earns a profit of ₹ 1 by selling one pen and incurs a loss of 40 paise per pencil while selling pencils of her old stock.

(i) In a particular month she incurs a loss of ₹ 5. In this period, she sold 45 pens. How many pencils did she sell in this period?

(ii) In the next month she earns neither profit nor loss. If she sold 70 pens, how many pencils did she sell?

Solution –

(i) Profit earned by selling one pen = ₹1
Profiteamed by selling 45 pens = ₹45, which we denote by +₹45
Total loss given = ₹5, which we denote by -₹5
Profit earned + Loss incurred = Total loss
Therefore, Loss incurred = Total Loss – Profit earned
=₹(-5-45)= ₹(-50) = -5000 paise
Loss incurred by selling one pencil = 40 paise which we write as -40 paise
So, number of pencils sold = (-5000)+(-40) = 125

(ii) In the next month there is neither profit nor loss.
So, Profit earned + Loss incurred = 0
i.e., Profit earned = -Loss incurred.
Now, profit earned by selling 70 pens = ₹70
Hence, loss incurred by selling pencils = 70 which we indicate by – ₹70 or 7,000 paise.
Total number of pencils sold = (-7000)÷ (-40) = 175 pencils.