Introduction to Linear Polynomials Class 9 Mathematics Ganita Manjari Solutions English Medium-Exercise Set 2.4

NCERT Solutions Class 9 Mathematics Ganita Manjari English Medium

Introduction to Linear Polynomials

Topic: Exercise Set 2.4

Exercise Set 2.4
Q1. Suppose a plant has height 1.75 feet and it grows by 0.5 feet each month.
(i) Find the height after 7 months.
(ii) Make a table of values for t varying from 0 to 10 months and show how the height, h, increases every month.
(iii) Find an expression that relates h and t, and explain why it represents linear growth.
Q2. A mobile phone is bought for ₹10,000. Its value decreases by ₹800 every year.
(i) Find the value of the phone after 3 years.
(ii) Make a table of values for t varying from 0 to 8 years and show how the value of the phone, v, depreciates with time.
(iii) Find an expression that relates v and t, and explain why it represents linear decay.
Q3. The initial population of a village is 750. Every year, 50 people move from a nearby city to the village.
(i) Find the population of the village after 6 years.

(ii) Make a table of values for t varying from 0 to 10 years and show how the population, P, increases every year.
(iii) Find an expression that relates P and t, and explain why it represents linear growth.
Q4. A telecom company charges ₹600 for a certain recharge scheme. This prepaid balance is reduced by ₹15 each day after the recharge.
(i) Write an equation that models the remaining balance b(x) after using the scheme for x days. Explain why it represents linear decay.
(ii) After how many days will the balance run out?
(iii) Make a table of values for x varying from 1 to 10 days and show how the balance b(x), reduces with time.

Solutions:

Q1. Suppose a plant has height 1.75 feet and it grows by 0.5 feet each month.

Solution:

Initial height of plant = 1.75 feet

Growth every month = 0.5 feet

(i) Height after 7 months

h = 1.75 + (0.5 × 7)

h = 1.75 + 3.5

h = 5.25 feet

So, the height after 7 months is 5.25 feet.

(ii) Table of values

t (months)     h (feet)
0              1.75
1              2.25
2              2.75
3              3.25
4              3.75
5              4.25
6              4.75
7              5.25
8              5.75
9              6.25
10             6.75

(iii) Expression relating h and t

h = 1.75 + 0.5t

This represents linear growth because the height increases by the same amount every month.

Q2. A mobile phone is bought for ₹10,000. Its value decreases by ₹800 every year.

Solution:

Initial value of phone = ₹10,000

Decrease every year = ₹800

(i) Value after 3 years

v = 10000 − (800 × 3)

v = 10000 − 2400

v = ₹7600

So, the value after 3 years is ₹7600.

(ii) Table of values

t (years)      v (₹)
0              10000
1              9200
2              8400
3              7600
4              6800
5              6000
6              5200
7              4400
8              3600

(iii) Expression relating v and t

v = 10000 − 800t

This represents linear decay because the value decreases by the same amount every year.

Q3. The initial population of a village is 750. Every year, 50 people move from a nearby city to the village.

Solution:

Initial population = 750

Increase every year = 50 people

(i) Population after 6 years

P = 750 + (50 × 6)

P = 750 + 300

P = 1050

So, the population after 6 years is 1050.

(ii) Table of values

t (years)      P
0              750
1              800
2              850
3              900
4              950
5              1000
6              1050
7              1100
8              1150
9              1200
10             1250

(iii) Expression relating P and t

P = 750 + 50t

This represents linear growth because the population increases by the same amount every year.

Q4. A telecom company charges ₹600 for a certain recharge scheme. This prepaid balance is reduced by ₹15 each day after the recharge.

Solution:

Initial balance = ₹600

Reduction every day = ₹15

(i) Equation representing remaining balance

b(x) = 600 − 15x

This represents linear decay because the balance decreases by the same amount every day.

(ii) Number of days after which balance becomes zero

600 − 15x = 0

15x = 600

x = 600/15

x = 40

So, the balance will run out after 40 days.

(iii) Table of values

x (days)       b(x)
1              585
2              570
3              555
4              540
5              525
6              510
7              495
8              480
9              465
10             450

NCERT Solutions Class 9 Hindi and English Medium – Complete Study Material

NCERT Solutions Class 9 students ke liye specially CBSE latest syllabus (2026-27) ke according prepare kiye gaye hain. Yeh solutions Hindi aur English medium dono ke liye available hain, jisse har student apni language preference ke hisaab se padh sakta hai. Har chapter ke sabhi prashnon ke step-by-step answers diye gaye hain jo concept clarity aur exam preparation me madad karte hain.

Chapter-Wise Detailed Explanations

Class 9 ke liye diye gaye Chapter Wise NCERT Solutions me har question ka detailed aur easy explanation diya gaya hai. Chahe aap CBSE Board Exam Preparation kar rahe ho ya school test ke liye revise kar rahe ho, yeh solutions aapko complete understanding denge. Har answer simple language me likha gaya hai jisse students concepts ko easily grasp kar saken.

Hindi and English Medium Support

Students Hindi aur English medium dono me NCERT Book Solutions Class 9 access kar sakte hain. Yeh dual language support un students ke liye helpful hai jo apni regional language me better samajhna chahte hain. Sabhi answers CBSE Latest Syllabus 2026-27 ke anusaar update kiye gaye hain.

Important Features of NCERT Solutions

• Class 9 NCERT Solutions PDF
• CBSE Class 9 Study Material
• NCERT Book Questions and Answers
• Exam Oriented Important Questions
• Step-by-Step Detailed Solutions
• Concept Clarity and Revision Notes

Why Students Should Use NCERT Solutions?

Aaj ke competitive environment me sirf textbook padhna kaafi nahi hota. NCERT Solutions for Class 9 students ko practice aur conceptual understanding dono provide karte hain. Yeh solutions unhe exam pattern samajhne, frequently asked questions practice karne aur high score achieve karne me madad karte hain. Regular practice se students apne weak topics ko improve kar sakte hain.

Best Resource for Exam Preparation

Agar aap Class 9 CBSE Preparation ke liye ek trusted aur reliable source dhundh rahe hain, to yeh NCERT Solutions perfect choice hain. Yeh study material school exams, unit tests, half-yearly aur annual exams ke liye equally useful hai. Har chapter ke answers accurate, verified aur student-friendly format me diye gaye hain.

Isliye agar aap NCERT Solutions Class 9 Hindi and English Medium search kar rahe hain, to yahan aapko complete chapter-wise solutions milenge jo aapki academic journey ko strong aur confident banayenge.