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: 27 (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 girls who speak English only ?

question_subject: 

Logic/Reasoning

question_exam: 

CAPF

stats: 

0,7,5,1,3,7,1

keywords: 

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

In this question, we are given that the ratio of boys to girls in the class is 5:7. This means there are 5x boys and 7x girls in the class.

Now, among the girls, 7 can speak both Hindi and English. Therefore, the number of girls who can only speak English is 7x - 7.

We are also given that 50% of the total students can speak only Hindi. So, the number of students who can speak only Hindi is 50% of 84, which is 42.

The ratio of the number of students speaking only Hindi to those speaking only English is 21:16. Let the number of students speaking only Hindi be 21y and the number of students speaking only English be 16y. Therefore, we can write the equation 21y + 16y = 42. Solving this equation, we get y = 1.

Now, we need to find the number of girls who speak English only. We know that the ratio of the number of boys speaking English only to the number of girls speaking English only is 3:5. So, the number of girls speaking English only is 5x.

Putting the value of x as 1