# CASE STUDY QUESTION 25-Class X-Maths

CASE STUDY QUESTION 25-Class X-Maths

**The department of Computer Science and Technology is conducting an International Seminar. In the seminar, the number of participants in Mathematics, Science and Computer Science are 60, 84 and 108 respectively. The coordinator has made the arrangement such that in each room, the same number of participants are to be seated and all of them being in the same subject. Also, they allotted the separate room for all the official other than participants.**

**(i) Find the total number of participants.**

(a) 60 (b) 84 (c) 108 (d) none of these**Sol:** Total number of participants = 60 + 84 + 108 = 252

**(ii) Find the LCM of 60, 84 and 108.**

(a) 12 (b) 504 (c) 544320 (d) 3780**Sol:** 60 = 2^{2} x 3 x 5

84 = 2^{2 }x 3 x 7

108 = 2^{2} x 3^{3}

LCM(60, 84, 108) = 2^{2 }x 3^{3 }x 5 x 7= 3780

**(iii) Find the HCF of 60, 84 and 108.**

(a) 12 (b) 60 (c) 84 (d) 108**Sol:** 60 = 2^{2} x 3 x 5

84 = 2^{2 }x 3 x 7

108 = 2^{2} x 3^{3}

HCF(60, 84, 108) = 2^{2} x 3= 12

**(iv) Find the minimum number of rooms required, if in each room, the same number of participants are to be seated and all of them being in the same subject.**

(a) 12 (b) 20 (c) 21 (d) none of these**Sol:** Minimum number of rooms required for all the participants = 252/12= 21

**(v) Based on the above (iv) conditions, find the minimum number of rooms required for all the participants and officials.**

(a) 12 (b) 20 (c) 21 (d) none of these**Sol:** Minimum number of rooms required for all = 21 + 1 = 22