Mathematics solution NCERT
Class 9 - Chapter 2: Introduction to Linear Polynomials
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 nth month.
Solution:
The student already has ₹500 in her account. Every month she receives ₹150 as pocket money. Therefore, her savings increase by ₹150 every month.
| Month | Amount in Account (₹) |
|---|---|
| 1st Month | 500 + 150 = 650 |
| 2nd Month | 500 + 2 × 150 = 800 |
| 3rd Month | 500 + 3 × 150 = 950 |
| 4th Month | 500 + 4 × 150 = 1100 |
| 5th Month | 500 + 5 × 150 = 1250 |
Thus, from the second month onwards:
- At the end of 2nd month = ₹800
- At the end of 3rd month = ₹950
- At the end of 4th month = ₹1100
- At the end of 5th month = ₹1250
If n represents the number of months, then
Amount = 500 + 150n
Linear Expression: 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:
Initially, the rally has 120 members. Every hour, 9 members leave the group.
| Hours | Calculation | Members Remaining |
|---|---|---|
| 1 | 120 − 9 | 111 |
| 2 | 120 − 18 | 102 |
| 3 | 120 − 27 | 93 |
| 4 | 120 − 36 | 84 |
| 5 | 120 − 45 | 75 |
The number of members decreases by 9 every hour.
If n represents the number of hours, then
Members Remaining = 120 − 9n
Linear Expression: 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:
Given:
Length = 13 cm
Area of Rectangle = Length × Breadth
| Breadth (cm) | Calculation | Area (cm²) |
|---|---|---|
| 12 | 13 × 12 | 156 |
| 10 | 13 × 10 | 130 |
| 8 | 13 × 8 | 104 |
Therefore:
- When breadth = 12 cm, Area = 156 cm²
- When breadth = 10 cm, Area = 130 cm²
- When breadth = 8 cm, Area = 104 cm²
If breadth is represented by b, then
Area = 13 × b
Linear Pattern: 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:
Given:
Length = 7 cm
Breadth = 11 cm
Volume of a Cuboid = Length × Breadth × Height
Volume = 7 × 11 × Height
Volume = 77 × Height
| Height (cm) | Calculation | Volume (cm³) |
|---|---|---|
| 5 | 77 × 5 | 385 |
| 9 | 77 × 9 | 693 |
| 13 | 77 × 13 | 1001 |
Therefore:
- Height 5 cm → Volume = 385 cm³
- Height 9 cm → Volume = 693 cm³
- Height 13 cm → Volume = 1001 cm³
If h represents the height, then
Volume = 77h
Linear Pattern: 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 per day = 20
| Days | Pages Read | Pages Left |
|---|---|---|
| 1 | 20 | 480 |
| 5 | 100 | 400 |
| 10 | 200 | 300 |
| 15 | 300 | 200 |
After 15 days:
Pages read = 20 × 15 = 300
Pages left = 500 − 300 = 200
Answer: 200 pages will be left after 15 days.
If d represents the number of days, then
Pages Left = 500 − 20d
Linear Pattern: P = 500 − 20d