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NCERT Class 9 Mathematics Exercise Set 2.3 Solutions: Introduction to Linear Polynomials

Step-by-step working for every question of Exercise Set 2.3 in NCERT's Class 9 Mathematics book, chapter “Introduction to Linear Polynomials”, written by Shishya. Each question is in our own short words; open the NCERT chapter for the exact wording and figures.

1. Ex 2.3 Q1

   A savings account has ₹500 and gets ₹150 at the end of every month. Amounts month by month, and a linear expression for the amount in the nth month.

   1. The initial amount in the savings account is ₹500.
   2. The amount added at the end of every month is ₹150.
   3. For the 1st month, the total amount is 500 + 150 × 1 = ₹650.
   4. For the 2nd month, the total amount is 500 + 150 × 2 = ₹800.
   5. For the 3rd month, the total amount is 500 + 150 × 3 = ₹950.
   6. For the nth month, the total amount is given by the linear expression 500 + 150n.

   Answer: Amounts for first three months: ₹650, ₹800, ₹950; Linear expression for nth month: 500 + 150n

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2. Ex 2.3 Q2

   A rally starts with 120 members and 9 leave every hour. Members left after 1, 2, 3 hours, and a linear expression for the end of the nth hour.

   1. The rally starts with 120 members.
   2. Every hour, 9 members leave the rally.
   3. After 1 hour, the number of members left is 120 − 9 × 1 = 111.
   4. After 2 hours, the number of members left is 120 − 9 × 2 = 102.
   5. After 3 hours, the number of members left is 120 − 9 × 3 = 93.
   6. After n hours, the number of members left is 120 − 9n.

   Answer: 111, 102, 93, 120 − 9n

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3. Ex 2.3 Q3

   A rectangle of length 13 cm: area when the breadth is (i) 12 cm, (ii) 10 cm, (iii) 8 cm, and the linear pattern for the area.

   1. The area of a rectangle is calculated by multiplying its length by its breadth.
   2. (i) For a breadth of 12 cm, the area is 13 × 12 = 156 cm².
   3. (ii) For a breadth of 10 cm, the area is 13 × 10 = 130 cm².
   4. (iii) For a breadth of 8 cm, the area is 13 × 8 = 104 cm².
   5. Let the breadth be b cm, so the area is 13 × b = 13b cm².

   Answer: (i) 156 cm²; (ii) 130 cm²; (iii) 104 cm²; linear pattern is 13b

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4. Ex 2.3 Q4

   A box 7 cm long and 11 cm broad: volume when the height is (i) 5 cm, (ii) 9 cm, (iii) 13 cm, and the linear pattern for the volume.

   1. The volume of a rectangular box is calculated by multiplying its length, breadth, and height.
   2. Here, the length is 7 cm and the breadth is 11 cm.
   3. (i) For a height of 5 cm, the volume is 7 × 11 × 5 = 385 cm³.
   4. (ii) For a height of 9 cm, the volume is 7 × 11 × 9 = 693 cm³.
   5. (iii) For a height of 13 cm, the volume is 7 × 11 × 13 = 1001 cm³.
   6. Let h represent the variable height of the box.
   7. The general expression for the volume is 7 × 11 × h, which simplifies to 77h.
      why?

      Simplifying (combining like terms, cancelling common factors) changes how the expression looks, not its value, so the next step is easier.

   Answer: (i) 385 cm³; (ii) 693 cm³; (iii) 1001 cm³; linear pattern: 77h

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5. Ex 2.3 Q5

   A 500-page book read at 20 pages a day: pages left after 15 days, and the linear pattern.

   1. Total pages in the book are 500.
   2. Pages read per day is 20.
   3. Let n be the number of days passed.
   4. Total pages read after n days is 20 × n.
   5. Pages left after n days is 500 − 20n.
   6. Substitute n = 15 to find pages left after 15 days.
      why?

      Putting the known values in place of the letters turns the formula or equation into plain arithmetic — the letters stood for exactly these values.

   7. Pages left = 500 − 20 × 15.
   8. Pages left = 500 − 300.
   9. Pages left = 200.

   Answer: 200; 500 − 20n

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