The average marks of boys in a class is 78.2 and that of girls in the same…
2020
The average marks of boys in a class is 78.2 and that of girls in the same class is 89.4. If the average marks of all the boys and girls in the class is 80.8, then the percentage of the number of girls in the class is:
- A.
23 3/14%
- B.
23 9/14%
- C.
33 9/14%
- D.
33 3/14%
Attempted by 1 students.
Show answer & explanation
Correct answer: A
CONCEPT
For a combined average, the total deviation below and above the combined average must balance. When one group average is below the combined average and another is above it, the group counts are in the inverse ratio of those deviations.
APPLICATION
Let the numbers of boys and girls be b and g. The combined-average equation is 78.2b + 89.4g = 80.8(b + g).
Move like terms: 89.4g - 80.8g = 80.8b - 78.2b, so 8.6g = 2.6b.
Therefore g:b = 2.6:8.6 = 13:43.
Total parts = 13 + 43 = 56, so the percentage of girls = 13/56 × 100 = 1300/56 = 325/14 = 23 3/14%.
CROSS-CHECK
Using 13 girl-parts and 43 boy-parts, the combined average is 89.4 × 13 + 78.2 × 43/56 = 80.8, so the percentage is consistent.
RESULT
The percentage of girls in the class is 23 3/14%.