In a class of 45 students, boys and girls are in the ratio of 5 : 4 respectively. The average marks obtained in mathematics out of 100 were 76 and that of girls were 78. What is the average marks of boys and girls together in mathematics (rounded-off to two decimal points)?
Answers
Answer:
76.89
Step-by-step explanation:
Let say boys and girls are 5x & 4x respectively
5x + 4x = 9x = 45
x = 5
Boys = 5*5 = 25
Grils = 4*5 = 20
Assuming 76 is average marks of boys as its not mentioned in question .
Total Marks of Boys = 25*76 = 1920
Total Mark of Girls = 20 * 78 = 1560
Total Marks of Boys + Girls = 1900 + 1560 = 3460
Average marks of boys + girls = 3460/45 = 76.89
average marks of boys and girls together in mathematics = 76.89
Answer:
76.89
Step-by-step explanation:
Ratio of boy : girls = 5 : 4 .
Let the number of boys be 5 x .
Let the number of girls be 4 x .
Given in the question :
Total number of students = 45 .
This implies that the sum of boys and girls = 45.
⇒ 5 x + 4 x = 45
⇒ 9 x = 45
⇒ x = 45/9
⇒ x = 5.
Hence the number of boys = 5 × 5 = 25 .
The number of girls = 4 × 5 = 20 .
The average marks of boys = 76 .
The average of marks of girls = 78 .
Average = sum of all observations / number of observations .
Number of girls = 20 .
Average = 78 .
⇒ 78 = sum of all marks of girls / 20
⇒ sum of marks of girls = 78 × 20
⇒ sum of marks of girls = 1560 .
Similarly :
Sum of marks of boys / 25 = 76
⇒ sum of marks of boys = 76 × 25
⇒ sum of marks of boys = 1900 .
Total marks = 1900 + 1560
= 3460 .
Average marks all together = sum / number of boys/girls .
⇒ Average = 3460 / 45
45 )3460( 76.888
315
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310
270
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400
360
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400
360
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400
360
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40
⇒ Average = 76.89