CBSE Class 10 Sample Paper for 2024 Boards - Maths Standard

Class 10
Solutions of Sample Papers for Class 10 Boards

## National Art convention got registrations from students from all parts of the country, of which 60 are interested in music, 84 are interested in dance and 108 students are interested in handicrafts. For optimum cultural exchange, organisers wish to keep them in minimum number of groups such that each group consists of students interested in the same artform and the number of students in each group is the same. Find the number of students in each group. Find the number of groups in each art form. How many rooms are required if each group will be allotted a room?

This question is similar to Question-2, Case-Based-Questions MCQ Chapter 1

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### Transcript

Now, Number of people interested in music = 60 Number of people interested in dance = 84 Number of people interested in handicrafts = 108 Finding number of students in each group Since we have to divide students into groups And the number of students in each group will be smaller than 60, 84 or 108 Thus, Number of students in each group = HCF of 60, 84, 108 Finding HCF So, 60 = 2 × 2 × 3 × 5 84 = 2 × 2 × 3 × 7 108 = 2 × 2 × 3 × 3 × 3 Thus, HCF = 2 × 2 × 3 = 12 So, Number of students in each group = 12 Find the number of groups in each art form Since, Number of people interested in music = 60 Number of people interested in dance = 84 Number of people interested in handicrafts = 108 And, Number of students in each group = 12 Now, Number of groups of music = 60/12 Number of groups of dance = 84/12 Number of groups of handicrafts = 108/12 Finding Number of rooms Since each group each group will be allotted a room Total number of rooms = Number of groups in music + dance + handicrafts = 5 + 7 + 9 = 21