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In a school having 400 students boys and girls are in the ratio of 3 : 5 respectively. The students speak Hindi, English or both the languages. 12% of the boys speak only Hindi, 22% of the girls speak only English. 24% of the total students speak only Hindi and the number of boys speaking both the languages is six times the number of boys speaking only Hindi.
What is the respective ratio between the number of boys and girls speaking both the languages?
The ratio of boys to girls is 3:5
There are 400 candidates in total.
So, the number of boys = $$\frac{3}{8}*400$$ = 150
Number of girls = $$\frac{5}{8}*400$$ = 250
Number of the boys speaking only Hindi = 12% * 150 = 18
Number of girls speaking only English = 22% * 250 = 55
Number of total students speaking only Hindi = 24% * 400 = 96
So, number of girls speaking only Hindi = 96 - 18 = 78
Number of boys speaking both languages = 6 * 18 = 108
But the total number of boys = boys speaking only Hindi + Boys speaking both languages + boys speaking only English
So, 150 = 18 + 108 + x
So, boys speaking only English = 24
the total number of girls = girls speaking only Hindi + girls speaking both languages + girls speaking only English
250 = 78 + x + 55
So, girls speaking both languages = 117
Number of boys speaking both languages : Number of girls speaking both languages = 108 : 117 = 12:13
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