Instructions

Study the information carefully to answer the question that follow:

A school consisting of a total of 1560 students has boys and girls in the ratio 7:5 respectively. All the students are enrolled in different types of hobby classes. viz: Singing, Dancing and Painting. One-fifth of the boys are enrolled in only Dancing classes.Twenty per cent of the girls are enrolled in only painting classes. Ten per cent of the boys are enrolled in only Singing classes. Twenty four per cent of the girls are enrolled in both Singing and Dancing classes together. The number of girls enrolled in only Singing classes is two hundred per cent of the boys are enrolled in the same. One thirteenth of the boys are enrolled in all the three classes together. The respective ratio of boys enrolled in Dancing and painting classes together to the girls enrolled in the same is 2:1 respectively. Ten per cent of the girls are enrolled in only Dancing classes whereas eight per cent of the girls are enrolled in both Dancing and painting classes together. The remaining girls are enrolled in all the three classes together. The number of boys enrolled in Singing and Dancing classes together is fifty per cent of the number of girls enrolled in the same. The remaining boys are enrolled in only painting classes.

Question 1

What is the total number of boys who are enrolled in Dancing ?

Solution

Total students = 1560

The ratio of boys to girls = 7:5

So, the number of boys = $$ \frac{7}{7+5}$$*1560 = 910

Number of girls = $$ \frac{5}{7+5}$$*1560 = 650

The number of students belonging to each category is as follows:

That answers the question.

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