Class 9 Maths Ganita Manjari Chapter 10 Exercise 10.1 Solutions How Quantities Combine: Understanding Data

The NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 10 Exercise 10.1 Part 2 – How Quantities Combine: Understanding Data help students understand how different quantities can be combined and compared using averages and related concepts. This part of the exercise focuses on applying these ideas to practical situations, helping students learn how to interpret data, calculate combined values, and reason with quantities of different sizes or weights.

The solutions are explained in a clear, step-by-step manner so that students can understand the method behind each answer and use the same approach for similar questions in exams and practice. Students can also refer to the Solutions PDF for easy access, revision, and practice anytime.

Class 9 Maths Ganita Manjari Chapter 10 Exercise 10.1 Solutions How Quantities Combine: Understanding Data

NCERT Class 9 Maths Ganita Manjari Chapter 10 Exercise Set 10.1

1. The average score of students on a test in Section A is 72 and that of students in Section B is 76. What is the combined average of both the sections given that Section A has 30 students and Section B has 25 students?

Answer:

Average score of Section A = 72
Number of students in Section A = 30

Total score of Section A = 72 × 30 = 2160

Average score of Section B = 76
Number of students in Section B = 25

Total score of Section B = 76 × 25 = 1900

Total score of both sections = 2160 + 1900 = 4060

Total number of students = 30 + 25 = 55

Combined Average = 4060 ÷ 55 = 73.82

Therefore, the combined average score of both sections is approximately 73.82.

2. A farmer mixes three equal quantities of fertilisers. The first one contains 1/10 nitrogen, the second contains 9/50 nitrogen, and the third contains 3/60 nitrogen. What is the fraction of nitrogen in the mixture?

Answer:

Since the farmer mixes equal quantities of all three fertilisers, the fraction of nitrogen in the mixture is the average of their nitrogen fractions.

First fertiliser = 1/10
Second fertiliser = 9/50
Third fertiliser = 3/60 = 1/20

Taking LCM = 100:

1/10 = 10/100
9/50 = 18/100
1/20 = 5/100

Total nitrogen fraction = 10/100 + 18/100 + 5/100 = 33/100

Since there are 3 equal quantities:

Fraction of nitrogen in the mixture = (33/100) ÷ 3 = 33/300 = 11/100

Therefore, the fraction of nitrogen in the mixture is 11/100.

3. (Śrīdharācārya, Pāṭīgaṇita, c. 750 CE) In ancient India, Varṇa was the measure of gold purity. A purity of 16 varṇa meant pure gold; in general, a purity of k varṇa meant that the gold-alloy was k/16 gold and the rest impurities. (Now the term used is karat; 16 Varṇa = 24 karat.) Suppose a goldsmith melts together three pieces of gold: 9 units at 12 varṇa, 5 units at 10 varṇa, and 17 units at 11 varṇa. Find the purity in varṇa of the combined gold.

Answer:

Since the three pieces have different weights, we use a weighted average.

Total gold content in varṇa-units:

9 × 12 = 108
5 × 10 = 50
17 × 11 = 187

Total = 108 + 50 + 187 = 345

Total weight of gold alloy:

9 + 5 + 17 = 31 units

Therefore,

Combined purity = 345/31 varṇa
= 11 4/31 varṇa
≈ 11.13 varṇa

Therefore, the purity of the combined gold is approximately 11.13 varṇa.

4. The average rainfall per day in the months of May, June, and July in a certain location are 3.5 mm, 10 mm, and 8.7 mm respectively. Write an expression that gives their combined average.

Answer:

Solution:

The average rainfall per day is:

  • May: 3.5 mm for 31 days
  • June: 10 mm for 30 days
  • July: 8.7 mm for 31 days

Since the months have different numbers of days, we use a weighted average.

Total rainfall in May:

31 × 3.5 = 108.5 mm

Total rainfall in June:

30 × 10 = 300 mm

Total rainfall in July:

31 × 8.7 = 269.7 mm

Therefore, total rainfall over the three months:

108.5 + 300 + 269.7 = 678.2 mm

Total number of days:

31 + 30 + 31 = 92 days

Combined average rainfall:

678.2 ÷ 92 ≈ 7.37 mm per day

Therefore, the combined average rainfall for May, June, and July is approximately 7.37 mm per day.

5. Calculate the concentration of spice mix in these two scenarios.

(i) A 100 mL kashayam/kadha with 5% spice mix, a 200 mL one with 10% spice mix, and a 300 mL one with 15% spice mix are combined.
(ii) A 300 mL kashayam/kadha with 5% spice mix, a 200 mL one with 10% spice mix, and a 100 mL one with 15% spice mix are mixed.

Answer:

The concentration of spice mix in the final mixture is:

Concentration = (Total amount of spice mix / Total volume of kashayam) × 100

(i)

For 100 mL kashayam with 5% spice mix:

Spice mix = 5% of 100 = 5 mL

For 200 mL kashayam with 10% spice mix:

Spice mix = 10% of 200 = 20 mL

For 300 mL kashayam with 15% spice mix:

Spice mix = 15% of 300 = 45 mL

Total spice mix = 5 + 20 + 45 = 70 mL

Total volume = 100 + 200 + 300 = 600 mL

Concentration = (70 / 600) × 100
= 11.67%

Therefore, the concentration of spice mix in scenario (i) is approximately 11.67%.

(ii)

For 300 mL kashayam with 5% spice mix:

Spice mix = 5% of 300 = 15 mL

For 200 mL kashayam with 10% spice mix:

Spice mix = 10% of 200 = 20 mL

For 100 mL kashayam with 15% spice mix:

Spice mix = 15% of 100 = 15 mL

Total spice mix = 15 + 20 + 15 = 50 mL

Total volume = 300 + 200 + 100 = 600 mL

Concentration = (50 / 600) × 100
= 8.33%

Therefore, the concentration of spice mix in scenario (ii) is approximately 8.33%.

Related Links: Chapter 10 Exercise-wise Solutions