Instructions

A school consisting of a total of 1560 students has boys and girls in the ratio of 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 percent of the girls are enrolled in only Painting classes.

Ten percent of the boys are enrolled in only Singing classes.

Twenty four percent of the girls are enrolled in both Singing and Dancing classes together.

The number of girls enrolled in only Singing classes is two hundred percent of the boys 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 percent of the girls are enrolled in only Dancing classes whereas eight percent 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 percent of the number of girls enrolled in the same.

The remaining boys are enrolled in only Painting classes.

Question 65

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

Solution

Boys : Girls = 7 : 5
No. of boys = 7/12 * 1560 = 910
No. of girls = 650
No. of boys enrolled in only Dancing = 910/5 = 182
No. of girls in only Painting = 650/5 = 130
No. of boys in only singing = 91
No. of girls in both singing and dancing = 24/100 * 650 = 156
No. of girls in only Singing = 91*2 = 182
No. of boys in all three = 1/13 * 910 = 70
No. of girls in both dancing and painting = 8/100 * 650 = 52
No. of girls in only dancing = 650/10 = 65
So, no. of boys in both dancing and painting = 2*52 = 104
No. of girls in all three = 65

No. of boys in both singing and dancing = 156/2 = 78
No. of boys in only painting = 385

​Total number of boys enrolled in Dancing = 434