Introduction to Linear Polynomials Class 9 Mathematics Ganita Manjari Solutions English Medium-Exercise Set 2.3

NCERT Solutions Class 9 Mathematics Ganita Manjari English Medium

Introduction to Linear Polynomials

Topic: Exercise Set 2.3

Solve the following:
Q1. A student has ₹500 in her savings bank account. She gets 150 every month as pocket money. How much money will she have at the end of every month from the second month onwards? Find a linear expression to represent the amount she will have in the n^th month.

Solution: 

A student has ₹500 in her bank account and gets ₹150 every month as pocket money.

Amount at the end of each month

After 1 month:

500 + 150 = 650

After 2 months:

500 + 2(150) = 800

After 3 months:

500 + 3(150) = 950

Pattern:

650, 800, 950,…

Linear Expression

If n is the number of months, then:

A = 500 + 150n

So, the amount in the n^th month is:

A = 500 + 150n

Q2. A rally starts with 120 members. Each hour, 9 members drop out of the group. How many members will remain after 1, 2, 3, … hours? Find a linear expression to represent the number of members at the end of the nth hour.

Solution: 

Initial members = 120
Every hour, 9 members leave.

Members remaining

After 1 hour:

120 − 9 = 111

After 2 hours:

120 − 18 = 102

After 3 hours:

120 − 27 = 93

Pattern:

111, 102, 93,…

Linear Expression

If n is the number of hours:

M = 120 − 9n

So, the number of members after nnn hours is:

M = 120 − 9n

Q3. Suppose the length of a rectangle is 13 cm. Find the area if the breadth is (i) 12 cm, (ii) 10 cm, (iii) 8 cm. Find the linear pattern representing the area of the rectangle.

Solution: 

Length = 13 cm

(i) b = 12 cm

When Breadth = 12 cm

Area = Length x breadth

Area = 13 cm x 12 cm 

         = 156 cm²

(ii) b = 10 cm 

When Breadth = 10 cm 

Area = Length x breadth

Area = 13 cm x 10 cm 

         = 130 cm²

(ii) b = 8 cm 

When Breadth = 8 cm 

Area = Length x breadth

Area = 13 cm x 8 cm 

         = 104 cm²

Linear Pattern

If breadth =b

A=13b

So, the linear expression for area is:

A=13b

Q4. Suppose the length of a rectangular box is 7 cm and breadth is 11 cm. Find the volume if the height is (i) 5 cm, (ii) 9 cm, (iii) 13 cm. Find the linear pattern representing the volume of the rectangular box.

Solution: 

Length = 7 cm
Breadth = 11 cm
Volume of rectangular box = Length × Breadth × Height
(i) h = 5 cm
When Height = 5 cm
Volume = Length × Breadth × Height
Volume = 7 cm × 11 cm × 5 cm
= 385 cm³
(ii) h = 9 cm
When Height = 9 cm
Volume = Length × Breadth × Height
Volume = 7 cm × 11 cm × 9 cm
= 693 cm³
(iii) h = 13 cm
When Height = 13 cm
Volume = Length × Breadth × Height
Volume = 7 cm × 11 cm × 13 cm
= 1001 cm³
Linear Pattern:
Volume = Length × Breadth × Height
V = 7 × 11 × h
V = 77h

Q5. Sarita is reading a book of 500 pages. She reads 20 pages every day. How many pages will be left after 15 days? Express this as a linear pattern.

Solution:

Total pages in the book = 500

Pages read every day = 20

Number of days = 15

Pages read in 15 days

= 20 × 15

= 300

Pages left after 15 days

= 500 − 300

= 200

So, 200 pages will be left after 15 days.

Linear Pattern:

Let the number of days be d.

Pages left = Total pages − Pages read

P = 500 − 20d

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