NCERT Solutions for Class 9 Maths Chapter 2 — Exercise Set 2.3#
A quantity that changes by the same fixed amount each step can be written as a linear expression $a n + b$, where $b$ is the starting value and $a$ is the constant change per step (positive for growth, negative for decay).
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. #
Solution
She starts with ₹500 and adds ₹150 every month, so at the end of the $n^{\text{th}}$ month she has:
$$A(n) = 500 + 150n$$| Month $n$ | Amount (₹) |
|---|---|
| 1 | 650 |
| 2 | 800 |
| 3 | 950 |
| 4 | 1100 |
| 5 | 1250 |
∴ The amount grows by ₹150 every month, and the linear expression is ₹$(500 + 150n)$.
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. #
Solution
The rally starts with 120 members and loses 9 every hour, so at the end of the $n^{\text{th}}$ hour:
$$M(n) = 120 - 9n$$| Hour $n$ | Members left |
|---|---|
| 1 | 111 |
| 2 | 102 |
| 3 | 93 |
| 4 | 84 |
| 5 | 75 |
∴ The number falls by 9 every hour, and the linear expression is $120 - 9n$.
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. #
Solution
Area $=$ length $\times$ breadth, and the length is 13 cm, so for a breadth of $b$ cm:
$$A = 13b$$| Breadth $b$ (cm) | Area $13b$ (cm²) |
|---|---|
| 12 | 156 |
| 10 | 130 |
| 8 | 104 |
∴ The areas are 156 cm², 130 cm² and 104 cm², and the linear pattern is $A = 13b$.
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. #
Solution
Volume $=$ length $\times$ breadth $\times$ height, so for a height of $h$ cm:
$$V = 7 \times 11 \times h$$$$\Rightarrow V = 77h$$
| Height $h$ (cm) | Volume $77h$ (cm³) |
|---|---|
| 5 | 385 |
| 9 | 693 |
| 13 | 1001 |
∴ The volumes are 385 cm³, 693 cm³ and 1001 cm³, and the 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. #
Solution
After $d$ days she has read $20d$ pages, so the number of pages left is:
$$P(d) = 500 - 20d$$We find $P(15)$:
$$= 500 - 20 \times 15$$$$= 500 - 300$$
$$= 200$$
∴ 200 pages are left after 15 days, and the linear pattern is $P = 500 - 20d$.