Question 26 - CBSE Class 10 Sample Paper for 2024 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at April 16, 2024 by Teachoo

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?

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

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

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