The average age of 80 girls was 20 years, the average age of 20 of them was 22 years and that of another 20 was 24 years. Find the average age of the remaining girls.

Options

A. 17 years
B. 19 years
C. 21 years
D. 15 years

Explanation

To find the average age of the remaining girls, we can follow these steps:

### Step 1: Calculate the total age of all 80 girls.
The average age of 80 girls is given as 20 years.
Total age of all girls = Average age × Number of girls = 20 years × 80 girls = 1600 years.

### Step 2: Calculate the total age of the first group of 20 girls.
The average age of the first group of 20 girls is 22 years.
Total age of the first group = Average age × Number of girls = 22 years × 20 girls = 440 years.

### Step 3: Calculate the total age of the second group of 20 girls.
The average age of the second group of 20 girls is 24 years.
Total age of the second group = Average age × Number of girls = 24 years × 20 girls = 480 years.

### Step 4: Calculate the total age of the remaining girls.
We have already calculated the total age of all girls (1600 years) and the total age of the two groups (440 years + 480 years).
Total age of the remaining girls = Total age of all girls - (Total age of first group + Total age of second group)
= 1600 years - (440 years + 480 years)
= 1600 years - 920 years
= 680 years.

### Step 5: Calculate the number of remaining girls.
Since there are 80 girls in total and 40 girls are accounted for in the two groups (20 + 20), the number of remaining girls = 80 - 40 = 40 girls.

### Step 6: Calculate the average age of the remaining girls.
Average age of remaining girls = Total age of remaining girls / Number of remaining girls
= 680 years / 40 girls
= 17 years.

### Final Answer:
The average age of the remaining girls is 17 years.

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