Class 9 Maths Ganita Manjari Chapter 10 Exercise 10.2 Solutions How Quantities Combine: Understanding Data

The NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 10 Exercise 10.2 Part 2 – How Quantities Combine: Understanding Data help students understand how different quantities can be combined and interpreted using concepts such as averages, weighted averages, proportions, and comparisons. The exercise includes practical, data-based questions that strengthen students’ analytical and problem-solving skills.

Each question is explained with clear, step-by-step solutions so that students can understand the method and apply it confidently to similar problems. Students can also refer to the Solutions PDF for convenient practice, revision, and exam preparation.

NCERT Class 9 Maths Ganita Manjari Chapter 10 Exercise Set 10.2

1. Savitri’s marks in Kashmiri are as follows: 35 out of 50 in internal tests, 44 out of 60 in the project, and 80 out of 100 in the final exam. The annual percentage score is calculated by combining the internals, project, and final exam in the ratio 3 : 4 : 5. Which of the following expression(s) gives her annual score (as a percentage) in Kashmiri?

(i) (35 × 3 + 44 × 4 + 80 × 5)/(3 + 4 + 5)
(ii) [(35/100) × 3 + (44/100) × 4 + (80/100) × 5]/(3 + 4 + 5)
(iii) [(35/50) × 3 + (44/60) × 4 + (80/100) × 5]/(3 + 4 + 5) × 100
(iv) [(35/50 × 100) × 3 + (44/60 × 100) × 4 + (80/100 × 100) × 5]/(3 + 4 + 5)

Class 9 Maths Ganita Manjari Chapter 10 Exercise 10.2 Solutions How Quantities Combine: Understanding Data

Answer:

Since the three components have different maximum marks, we must first convert each score into a percentage before applying the ratio 3 : 4 : 5.

Internal tests:

35/50 × 100 = 70%

Project:

44/60 × 100 = 73.33%

Final exam:

80/100 × 100 = 80%

Now, taking the weighted average:

Annual score
= [(70 × 3) + (73.33 × 4) + (80 × 5)] / (3 + 4 + 5)

= (210 + 293.33 + 400) / 12

= 903.33 / 12

≈ 75.28%

Now checking the given expressions:

  • (i) Incorrect, because it uses the raw marks directly even though the maximum marks are different.
  • (ii) Incorrect, because 35, 44, and 80 are not all marks out of 100.
  • (iii) Correct, because each score is first written as a fraction of its respective maximum marks.
  • (iv) Correct, because each score is first converted into a percentage before taking the weighted average.

Therefore, the correct expressions are (iii) and (iv), and Savitri’s annual score is approximately 75.28%.

Related Links: Chapter 10 Exercise-wise Solutions