Question

In a certain class two-thirds of the female students and half of the male students speak Oriya. If there are three-fourth as many girls as boys in the class, what fraction of the entire class speak Odia ?​

Answer 1

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Let

Number of Students speak Odia = O

Number of boys = B

Number of girls = G

Total number of students = T

Number of Odia speaking students are 1/2 of boys and 2/3 of girls.

There are 3/4 girls as boys.

O = 1/2 B + 2/3 G

3/4 B = G

Substituting equation 2 in equation 1 for G.

O = 1/2 B + 3/4 G = 3/4 B

O = B ( 1/2 × 2/3 × 3/4)

O = B (1)

O = B

The number of students who speak Odia are equal to the number of boys.

And the total number of students must be equal to the total number of boys and total number of girls.

T = B + G

T = G + 3/4 B

T = B ( 1 + 3/4)

T = 7/4 or 1 3/4

The fraction of students who speak Odia in the entire class is the ratio of "Number of students speak French" to "Total number of students".

Fraction = Number of students speaking Odia ÷ Total number of students

Fraction = F/T

Fraction = B / (7/4 B)

Fraction = 4/7

Answer is 4/7.