Exercise Set 2.3 Class 9 · Ganita Manjari
📘 Chapter 2 — Polynomials
📌 Linear Patterns & Expressions
📐
A linear expression is of the form an + b, where a and b are constants and n is a variable.
It represents a constant rate of change.
1
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 nᵗʰ month.
Initial amount in bank = ₹500
Monthly pocket money = ₹150
At the end of:
2nd month = 500 + 2(150) = ₹800
3rd month = 500 + 3(150) = ₹950
4th month = 500 + 4(150) = ₹1100
and so on…
3rd month = 500 + 3(150) = ₹950
4th month = 500 + 4(150) = ₹1100
and so on…
Let the amount in the nᵗʰ month be Aₙ
Then, Aₙ = 500 + 150n
✅
Thus, the required linear expression is: Aₙ = 150n + 500
2
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.
Initial members = 120
Members leaving each hour = 9
After:
1 hour = 120 − 9 = 111
2 hours = 120 − 18 = 102
3 hours = 120 − 27 = 93
2 hours = 120 − 18 = 102
3 hours = 120 − 27 = 93
Let number of members after n hours = Mₙ
Mₙ = 120 − 9n
✅
Thus, required linear expression is Mₙ = 120 − 9n.
3
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.
Length = 13 cm
Area = Length × Breadth
(i)
Breadth = 12 cm
Area = 13 × 12 = 156 cm²
(ii)
Breadth = 10 cm
Area = 13 × 10 = 130 cm²
(iii)
Breadth = 8 cm
Area = 13 × 8 = 104 cm²
Let breadth = x cm
Area = 13x
✅
Thus, linear pattern is A = 13x.
4
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.
Length = 7 cm, Breadth = 11 cm
Volume = Length × Breadth × Height
= 7 × 11 × h
= 77h
= 77h
(i)
Height = 5 cm
Volume = 77 × 5 = 385 cm³
(ii)
Height = 9 cm
Volume = 77 × 9 = 693 cm³
(iii)
Height = 13 cm
Volume = 77 × 13 = 1001 cm³
Let height = h cm
Volume = 77h
✅
Thus, linear pattern is V = 77h.
5
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.
Total pages = 500
Pages read per day = 20
Pages read in 15 days = 20 × 15 = 300
Pages left = 500 − 300 = 200
Let pages left after n days = Pₙ
So, Pₙ = 500 − 20n
✅
Thus, linear pattern is Pₙ = 500 − 20n.
📖
After 15 days: P₁₅ = 500 − 20(15) = 500 − 300 = 200 pages left.