In a class of 60 students, the average age of 25 girls is 12 yr and boys is 14 yr. Two of the students aged 16 and 14 yr leave the class and are replaced by 3 students of ages 12,11 and 10 yr, Find the change in average age of the class.

Options

A. 0.167 yr
B. 0.45 yr
C. 1.2 yr
D. 1 yr

Answer

To solve the problem step by step, we will calculate the initial average age of the class, the effect of the students leaving, and the new average age after the replacements.

### Step 1: Calculate the total age of girls and boys

1. **Total number of students**: 60
2. **Number of girls**: 25
3. **Average age of girls**: 12 years
4. **Number of boys**: 60 - 25 = 35
5. **Average age of boys**: 14 years

**Total age of girls** = Average age of girls × Number of girls
= 12 years × 25 = 300 years

**Total age of boys** = Average age of boys × Number of boys
= 14 years × 35 = 490 years

**Total age of the class** = Total age of girls + Total age of boys
= 300 + 490 = 790 years

### Step 2: Calculate the initial average age of the class

**Initial average age of the class** = Total age of the class / Total number of students
= 790 years / 60 students = 13.167 years (approximately)

### Step 3: Calculate the effect of students leaving and new students joining

1. **Ages of students leaving**: 16 years and 14 years
**Total age of students leaving** = 16 + 14 = 30 years

2. **Ages of new students joining**: 12 years, 11 years, and 10 years
**Total age of new students joining** = 12 + 11 + 10 = 33 years

### Step 4: Calculate the new total age of the class

**New total age of the class** = Old total age - Total age of students leaving + Total age of new students joining
= 790 - 30 + 33
= 790 - 30 + 33 = 793 years

### Step 5: Calculate the new total number of students

**New total number of students** = Old total number of students - Students leaving + New students joining
= 60 - 2 + 3 = 61 students

### Step 6: Calculate the new average age of the class

**New average age of the class** = New total age of the class / New total number of students
= 793 years / 61 students ≈ 13.0 years (approximately)

### Step 7: Calculate the change in average age

**Change in average age** = New average age - Old average age
= 13.0 - 13.167 ≈ -0.167 years

### Conclusion

The change in average age of the class is approximately -0.167 years.

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