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This section has $3$ case study based questions carrying $4$ marks each.
Case Study – 1
The science department of a college is conducting an international seminar in which the number of participants in Physics, Chemistry and Biology are $65, 91$ and $117$ respectively. The coordinator has made the arrangement such that in each room, the same number of participants are to be seated with all of them being in the same subject.
Based on the information given above, answer the following questions :
(i) Find the HCF of $65, 91$ and $117$.
(ii) Find the LCM of $65, 91$ and $117$.
(iii) (a) Find the minimum number of rooms required based on the above conditions.
OR
(iii) (b) Find the minimum number of participants to be accommodated in each of the rooms.
Case Study – 1
The science department of a college is conducting an international seminar in which the number of participants in Physics, Chemistry and Biology are $65, 91$ and $117$ respectively. The coordinator has made the arrangement such that in each room, the same number of participants are to be seated with all of them being in the same subject.
Based on the information given above, answer the following questions :
(i) Find the HCF of $65, 91$ and $117$.
(ii) Find the LCM of $65, 91$ and $117$.
(iii) (a) Find the minimum number of rooms required based on the above conditions.
OR
(iii) (b) Find the minimum number of participants to be accommodated in each of the rooms.
Show SolutionHide Solution↓
(i) $65 = 5 \times 13$; $91 = 7 \times 13$ ; $117 = 3^2 \times 13$
HCF $(65, 91 \& 117) = 13$
(ii) LCM $(65, 91 \& 117) = 3^2 \times 5 \times 7 \times 13 = 4095$
(iii) (a) minimum number of rooms = $\frac{65}{13} + \frac{91}{13} + \frac{117}{13}$
$= 21$
OR
(b) $1$
HCF $(65, 91 \& 117) = 13$
(ii) LCM $(65, 91 \& 117) = 3^2 \times 5 \times 7 \times 13 = 4095$
(iii) (a) minimum number of rooms = $\frac{65}{13} + \frac{91}{13} + \frac{117}{13}$
$= 21$
OR
(b) $1$