Question

In a sitting arrangement, some people are made to sit in 9 rows such that each row has 4 people. If the same number of people are rearranged in ‘m’ rows with ‘n’ number of people in each row, find the possible values of mand n.

Answer 1

The possible values of a new number of people (n) in each row with m rows are 1× 36, 2×18, 3×12,4× 9, and 6×6.

Given:

9 rows with 4 people each in it.

To Find:

The possible value of m and n.

Solution:

Total number of peoples = 9 * 4 = 36.

The number  36 can be written as 1× 36, 2×18, 3×12,4× 9, and 6×6.

When m= 1, n= 36

⇒In 1 row with 36 persons in it.

When m = 2 , n=18

⇒In 2 rows with 18 persons each in it.

When m= 3 , n=12

⇒In 3 rows with 12 persons each in it.

When m = 4 , n=9

⇒In 4 rows with 9 persons each in it.

When m =6 , n=6

⇒In 6 rows with 6 persons each in it.

Therefore, The possible values of a new number of people (n) in each row with m rows are 1× 36, 2×18, 3×12,4× 9, and 6×6.

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Answer 2

Answer:

The possible values of m and n are 1,2,3,4,6,9,12,18,36

Step-by-step explanation:

Given,

Number people in each row = 4 people

Total number of rows = 9

The same number of people is arranged in 'm' row and 'n' columns.

To find,

The possible values of 'm' and 'n'

Solution:

Since there are 9 rows and each row contains 4 people, the total number of people in the arrangement = 9×4 = 36

Since the same number of people are arranged in 'm' rows and 'n' columns, the possible values of 'm' and 'n' can be calculated by the pair factors of 36

The pair of factors of 36 are (1,36),(2,18),(3,12), (4,9),(6,6)(9,4)(12,3),(18,2)(1,36)

Hence the possible pair of combinations of (m,n) are(1,36),(2,18),(3,12), (4,9),(6,6)(9,4)(12,3),(18,2)(1,36)

∴The possible values of m and n are 1,2,3,4,6,9,12,18,36

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