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: 26 (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 number of boys who speak both the languages ?

question_subject: 

Logic/Reasoning

question_exam: 

CAPF

stats: 

0,11,7,0,4,11,3

keywords: 

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

In this problem, we are given the number of students in a class and their language abilities. We are also given the ratios of boys to girls and a few other language-related ratios.

First, let`s calculate the number of boys and girls in the class. We know that the ratio of boys to girls is 5:7, which means there are 5x boys and 7x girls. Here, x represents a common factor of the number of boys and girls.

Next, we are told that 50% of the total students can speak only Hindi. This implies that half of the total number of students speak only Hindi and the other half may speak both Hindi and English. Let`s call the number of students who speak only Hindi as H and the number of students who speak both Hindi and English as HE.

We are also given that the ratio of the number of students speaking only Hindi to that speaking only English is 21:16. This implies that 21x students speak only Hindi and 16x students speak only English.

Now, let`s consider the ratio of the number of boys speaking English only to that of girls speaking English only. We are told that the ratio is 3:5. This means that 3x boys speak only English and