Q) In a seminar , the numbers of participants in English , German and Sanskrit are 45, 75 and 135. Find the numbers of rooms required to house them , if in each room the same number of participants are to be accommodated and they should be of the same language

• 1) 45
• 2) 17
• 3) 75
• 4) 135

Since , each room , the same number of participants , of the same language , are to be accommodated , their number in each room
HCF of 45 , 75 and 135
HCF ( 45 , 75 , 135 ) = 15
Each room accommodates 15 participants
\(\implies\) Total number of rooms required for English = \(\frac{45}{15}\) = 3
\(implies\) Total number of rooms required for German = \(\frac{75}{15}\) = 5
\(\implies\) Total number of rooms required for sanskrit = \(\frac{135}{15}\) = 9
\(\implies\) = Total number of rooms = \(3 + 5 + 9 = 17\)