Question

In a six days national level seminar from 12th August 2019 to 17th August 2019, the number of participants in Science and English are 60, and 108 respectively. The participants of 6 regions are coming. For every region, minimum number of participants for Science and English are 6 and 10 respectively. Q(a) What will be the possible maximum numbers of participants from a region for Science? b) Find the minimum number of rooms required if in each room the same numbers of participants are seated and all of them being in the same subject. c) What is the minimum numbers of participants in English for any region if highest number of participants for any region is 19?​

Answer 1

(a) The maximum possible number of participants from a region for science = 30

(b) The minimum number of rooms required if in each room the same numbers of participants are seated and all of them being in the same subject = 14

(c) The minimum numbers of participants in English for any region if highest number of participants for any region is 19 = 13

Step-by-step explanation:

The no of region = 6

The number of participants of Science = 60

The number of participants of English = 108

Minimum no. of participants of Science for a region = 6

Minimum no. of participants of English for a region = 10

(a) The maximum possible number of participants from a region for science

If there are 6 (minimum) participants from 5 region

Then The 6th region should have 60 - 6 × 5 = 60 - 30 = 30 participants

Thus, the maximum possible number of participants from a region for science = 30

(b) The minimum number of rooms required if in each room the same numbers of participants are seated and all of them being in the same subject

First we need to calculate HCF of 60 and 108

$60=2^2\times 3\times 5$

$108=2^2\times 3^3$

Therefore, HCF = $2^2\times 3=12$

Thus, 12 participants must be in a room

Therefore, minimum number of rooms

$=\frac{60}{12}+\frac{108}{12}$

$=5+9$

$=14$

(c) The minimum numbers of participants in English for any region if highest number of participants for any region is 19

If 5 region has highest participants for English

Then the 6th region will have = 108 - 5 × 19 = 13 participants

Thus, the minimum numbers of participants in English for any region = 13

Hope this answer is helpful.

Know More:

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