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: 29 (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. How many girls can speak Hindi ?

question_subject: 

Logic/Reasoning

question_exam: 

CAPF

stats: 

0,5,8,6,1,1,5

keywords: 

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

To solve this problem, we need to break it down into different parts. Let`s analyze each part of the information given:

1. In a class of 84 students, boys and girls are in the ratio of 5:7. This means that there are 5/12 boys and 7/12 girls in the class.

2. Among the girls, 7 can speak Hindi and English. This indicates that 7/12 of the girls can speak both languages.

3. 50% of the total students can speak only Hindi. So, 50% of 84 is 42 students who can speak only Hindi.

4. The ratio of students speaking only Hindi to those speaking only English is 21:16. Let`s assume the number of students speaking only Hindi is 21x, and the number of students speaking only English is 16x.

5. The ratio of boys speaking English only to girls speaking English only is 3:5. So, assuming the number of boys speaking English only is 3y, and the number of girls speaking English only is 5y.

Now, let`s solve the problem:

Since there are 84 students, the number of boys is (5/12) * 84 = 35