Class 9 Mathematics Ganita Manjari Part 1 NCERT Solutions
Chapter-2: Introduction to Linear Polynomials

Exercise Set 2.3

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 n^{th} month.
Solution:
Initial amount in bank account =₹500 
Monthly Pocket money =₹150 
After the 1st month =500+150=₹650 
After the 2nd month =500+150+150=₹800 
After the 3rd month =500+150+150+150=₹950 

Therefore, the required amounts are ₹650,\ ₹800,\ ₹950,\ldots 

Let the amount at the end of the n^{th} month be A_n. 
∴ A_n=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 n^{th} hour.
Solution:
Initial number of members =120
Members drop out every hour =9
After 1 hour =120-9=111
After 2 hours =120-18=102
After 3 hours =120-27=93
…
Let the number of members at the end of the n^{th} hour be M_n.
Therefore, M_n=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:
Length of the rectangle =13\text{ cm}
    \text{Area}=\text{Length}\times\text{Breadth} 

(i) Breadth = 12 cm 
    \text{Area}=13\times12 
             =156\text{ cm}^2 

(ii) Breadth = 10 cm 
    \text{Area}=13\times10 
             =130\text{ cm}^2 

(iii) Breadth = 8 cm 
       \text{Area}=13\times8 
                =104\text{ cm}^2 

Let the breadth be ‘b\text{ cm}’, then linear expression representing the area ‘A’ 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:
Length =7\text{ cm} 
Breadth =11\text{ cm}
\text{Volume}=\text{Length}\times\text{Breadth}\times\text{Height}
\text{Volume}= 7\times11 \times\text{Height}
\text{Volume}=77\times\text{Height} 

(i) Height = 5 cm 
Volume=77\times5 
=385\text{ cm}^3 

(ii) Height = 9 cm 
Volume=77\times9 
=693\text{ cm}^3 

(iii) Height = 13 cm 
Volume=77\times13 
=1001\text{ cm}^3 

Let the height be ‘h\text{ cm}’, then linear expression representing the volume ‘V’ is: 
     V=13h 

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 number of pages =500 
Pages read every day =20 
Pages left after 1 day =500-20=480 
Pages left after 2 days =500-20-20=460 
Pages left after 3 days =500-20-20-20=440 
… 
Pages left after 15 days =500-20(15) 
                                           =500-300 
                                           =200 

Let the pages left after n days =P_n 
∴ P_n=500-20n