Half the students of a class are dancing and three-fourths of the remaining are playing cricket. If the remaining 9 students are studying in the library, then find the total number of students in the class.

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Solution

Let the total number of students be $x$

According to the question,
Number of students dancing $= \frac{x}{2}$

Number of students remaining $= x - \frac{x}{2}$
$= \frac{x}{2}$

Students playing cricket
$= (\frac{3}{4}) (\frac{x}{2})$
$= \frac{3 x}{8}$

Remaining students $= 9$

$\Rightarrow (x - \frac{x}{2}) - \frac{3 x}{8} = 9 \Rightarrow \frac{x}{8} = 9 \Rightarrow x = 8 \times 9 \Rightarrow x = 72$

Hence, the total number of students in the class = 72

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Study the information carefully to answer the questions:

A school consisting of a total of 1560 students has boys and girls in the ratio of 7:5. 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 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 ratio of boys enrolled in Dancing and Painting classes together to the girls enrolled in the same is 2:1. 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 Singing and Dancing 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.

What is the total number of students enrolled in all the three classes together?

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Half the students of a class are dancing and three-fourths of the remaining are playing cricket. If the remaining 9 students are studying in the library, then find the total number of students in the class.

Let the total number of students be x According to the question, Number of students dancing =x2 Number of students remaining =x−x2 =x2 Students playing cricket =(34)(x2) =3x8 Remaining students =9 ⇒ (x−x2)−3x8=9⇒ x8=9⇒ x=8×9⇒ x=72 Hence, the total number of students in the class = 72