Answered

24. As part of their project, Nadia and Raju conducted a survey on [tex]\(10\% \)[/tex] of the number of students in Class A and on [tex]\(70\% \)[/tex] of the number of students in Class B.

(a) Nadia said that [tex]\(10\% + 70\% \)[/tex], i.e. [tex]\(80\%\)[/tex], of the total number of students in the two classes had done the survey. Is she correct? Explain your answer.

(b) Raju, however, said that [tex]\(\frac{10\% + 70\%}{2} \)[/tex], i.e. [tex]\(40\%\)[/tex], of the total number of students in the two classes had done the survey. Is he correct? Explain your answer.



Answer :

GinnyAnswer
Sure, let's tackle this problem step by step.

### Given Information:
- Class A has 100 students.
- Class B has 100 students.
- Nadia surveyed 10% of Class A.
- Nadia also surveyed 70% of Class B.

### Step 1: Calculate the Number of Students Surveyed in Each Class
Class A:
- The number of students surveyed in Class A = 10% of 100
[tex]\[ \text{Class A surveyed} = \frac{10}{100} \times 100 = 10 \][/tex]

Class B:
- The number of students surveyed in Class B = 70% of 100
[tex]\[ \text{Class B surveyed} = \frac{70}{100} \times 100 = 70 \][/tex]

### Step 2: Total Number of Students Surveyed
[tex]\[ \text{Total students surveyed} = \text{Class A surveyed} + \text{Class B surveyed} = 10 + 70 = 80 \][/tex]

### Step 3: Total Number of Students in Both Classes
[tex]\[ \text{Total students} = \text{Class A students} + \text{Class B students} = 100 + 100 = 200 \][/tex]

### Step 4: Percentage of Total Students Surveyed
To find the percentage of the total number of students surveyed:
[tex]\[ \text{Percentage surveyed} = \left( \frac{\text{Total students surveyed}}{\text{Total students}} \right) \times 100 \][/tex]
[tex]\[ \text{Percentage surveyed} = \left( \frac{80}{200} \right) \times 100 = 40\% \][/tex]

### Part (a)
Nadia claimed that [tex]\(10\% + 70\% = 80\%\)[/tex] of the total students were surveyed. Let's check this:

Nadia's Claim:
- She claimed that 80% of the total students in both classes were surveyed.
- However, we calculated that only 40% of the total students were surveyed.

Conclusion:
Nadia's claim is incorrect because only 40% of the total students were actually surveyed, not 80%.

### Part (b)
Raju's approach involved taking the average of the percentages:

[tex]\[ \text{Raju's calculation} = \frac{10\% + 70\%}{2} = \frac{80\%}{2} = 40\% \][/tex]

Raju's Claim:
- He claimed that 40% of the total students in both classes were surveyed.
- Our calculation confirms that indeed 40% of the total students were surveyed.

Conclusion:
Raju's claim is correct because 40% of the total number of students were actually surveyed, which matches his calculation.

Other Questions