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One-third of the students of a class hav...

One-third of the students of a class have chosen to play cricket. One-half of the students who have chosen to play cricket have also opted for painting classes. What fraction of students of the class have opted for painting class? If there are `30` students in the class, how many students have opted for a. cricket? b. painting class?

A

a. = `15` students.
b. = `5` students.

B

a. = `10` students.
b. = `5` students.

C

a. = `5` students.
b. = `5` students.

D

a. = `10` students.
b. = `9` students.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, we will break down the information given and perform the necessary calculations. ### Step 1: Determine the total number of students who play cricket. The problem states that one-third of the students have chosen to play cricket. **Calculation:** - Total number of students in the class = 30 - Students who chose cricket = (1/3) * Total students = (1/3) * 30 = 10 **Hint:** To find one-third of a number, divide the number by 3. ### Step 2: Determine the number of students who opted for painting classes. Next, we know that one-half of the students who have chosen to play cricket have also opted for painting classes. **Calculation:** - Students who opted for painting = (1/2) * Students who chose cricket = (1/2) * 10 = 5 **Hint:** To find one-half of a number, divide the number by 2. ### Step 3: Find the fraction of students who opted for painting classes. Now, we need to express the number of students who opted for painting as a fraction of the total number of students in the class. **Calculation:** - Fraction of students who opted for painting = Students who opted for painting / Total students = 5 / 30 - Simplifying the fraction: - Divide both the numerator and the denominator by 5. - (5 ÷ 5) / (30 ÷ 5) = 1/6 **Hint:** To simplify a fraction, divide both the numerator and denominator by their greatest common divisor (GCD). ### Final Answers: a. Number of students who opted for cricket = 10 b. Number of students who opted for painting class = 5 c. Fraction of students who opted for painting = 1/6
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