Exercise 2.3 focuses on understanding linear patterns and forming algebraic expressions in real-life situations. In this exercise, students learn how quantities change uniformly and how to represent them using linear equations. Below are the step-by-step solutions to all questions, explained in a simple and student-friendly manner.
Exercise 2.3 Solutions
Question 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
Initial amount = ₹500
Monthly increase = ₹150
After n months: A=500+150n
Now calculate:
- 2nd month → ₹500 + 150×2 = ₹800
- 3rd month → ₹950
- 4th month → ₹1100
- Linear expression is
A=500+150n
Question 2
A rally starts with 120 members. Each hour, 9 members drop out. How many members remain after 1, 2, 3, … hours? Find a linear expression.
Solution
Initial members = 120
Decrease per hour = 9
After n hours: M=120−9n
Members left after
- 1 hour =111
- 2 hours = 102
- 3 hours = 93
Linear expression is:
M=120−9n
Question 3
Suppose the length of a rectangle is 13 cm. Find the area if breadth is (i) 12 cm, (ii) 10 cm, (iii) 8 cm. Find the linear pattern.
Solution
Area of rectangle =Length×Breadth
Given length = 13 cm
(i) b = 12 so Area = 13×12 = 156 cm²
(ii) b = 10 so Area = 130 cm²
(iii) b = 8 so Area = 104 cm²
Linear expression:
A=13b
Question 4
Suppose the length of a rectangular box is 7 cm and breadth is 11 cm. Find the volume if height is (i) 5 cm, (ii) 9 cm, (iii) 13 cm. Find the linear pattern.
Solution
Volume of rectangular box (cuboid)=l×b×h
Given: V=7×11×h=77h
(i) h = 5 so V = 77×5= 385 cm³
(ii) h = 9 so V = 77×9= 693 cm³
(iii) h = 13 so V = 77×13= 1001 cm³
Linear expression:
V=77h
Question 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
Total pages = 500
Pages read per day = 20
Pages left after n days =500−20n
Pages left after 15 days =500−20(15)
=200
So Pages left after 15 days are 200
Linear expression:
P=500−20n
Conclusion
This exercise helps students understand how to convert real-life situations into linear equations. Mastering these concepts builds a strong foundation for algebra and higher mathematics.