In a class of 84 students, boys and girls are in the ratio of 5 : 7. Among the girls 7 can speak Hindi and English, 50 per cent of the total students can speak only Hindi, The ratio of the number of students speaking only Hindi to that speaking only Engli

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Q: 30 (CAPF/2011)
In a class of 84 students, boys and girls are in the ratio of 5 : 7. Among the girls 7 can speak Hindi and English, 50 per cent of the total students can speak only Hindi, The ratio of the number of students speaking only Hindi to that speaking only English is 21 : 16. The ratio of the number of boys speaking English only to that of girls speaking English only is 3 : 5.What is the ratio of the number of boys who speak English to that of girls who do so ?

question_subject: 

Logic/Reasoning

question_exam: 

CAPF

stats: 

0,7,8,7,4,4,0

keywords: 

{'ratio': [1, 0, 1, 12], 'total students': [0, 0, 0, 5], 'students': [0, 1, 1, 1], 'hindi': [7, 7, 4, 13], 'number': [0, 0, 0, 2], 'per cent': [0, 1, 0, 0], 'girls': [0, 2, 3, 10], 'boys': [0, 1, 5, 11], 'english': [1, 0, 0, 0], 'class': [4, 1, 4, 15]}

To solve this problem, let`s start by finding the number of boys and girls in the class. We are given that the ratio of boys to girls is 5:7. Let`s assume the common ratio between the two is x.

So, the number of boys in the class = 5x and the number of girls = 7x.

Now, among the girls, 7 can speak Hindi and English. This means 7 girls speak both languages.

We are also given that 50% of the total students can speak only Hindi. Let`s assume this number to be y.

So, the number of students who can speak only Hindi = y.

The ratio of the number of students speaking only Hindi to that speaking only English is 21:16. This means the number of students speaking only English = (21/16)y.

Now, let`s find the number of boys and girls speaking only English.

The ratio of boys speaking only English to girls speaking only English is 3:5. This means the number of boys speaking only English = (3/5) * (21/16)y.

The number of girls speaking only English = (5/5) * (21/16)y.

Finally, we can find the ratio of boys who