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Q.

The students of a class are made to stand in rows. If 3 students are extra in a row, there would be 1 row less. If 3 students are less in a row, there would be 2 rows more. Find the number of students in the class.

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a

the total number of students in the class is 36.

b

the total number of students in the class is 35.

c

the total number of students in the class is 42.

d

the total number of students in the class is 51.

answer is A.

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Detailed Solution

Given that the students of a class are made to stand in rows.
Also given, if 3 students are extra in a row, there would be 1 row less and if 3 students are less in a row, there would be 2 rows more.
Let us assume the number of rows be y and number of students in a row be x.
Total students of the class = Number of rows

×

Number of students in a row
Total students of the class = xy
When 3 student extra in a row and 1 row less, then
Total number of students

= y − 1 x + 3

.

⇒ x y = y − 1 x + 3

⇒ x y = y x + 3 − 1 x + 3

⇒ x y = y x + 3 y − x − 3

⇒ 3 y − x − 3 = 0

⇒ 3 y − x = 3

⇒ − x + 3 y = 3

…………,...(1)
When 3 student less in a row and 2 row more, then
Total number of students

= y + 2 x − 3

.

⇒ x y = y + 2 x − 3

⇒ x y = y x − 3 + 2 x − 3

⇒ x y = x y − 3 y + 2 x − 6

⇒ 0 = − 3 y + 2 x − 6

⇒ 2 x − 3 y = 6

………….. (2)
Multiply equation (1) by 2.

⇒ − x + 3 y = 3

⇒ − 2 x + 6 y = 6

………………..(3)
Add equation (2) and (3).

⇒ 2 x − 3 y + − 2 x + 6 y = 6 + 6

⇒ 2 x − 3 y − 2 x + 6 y = 12

⇒ − 3 y + 6 y = 12

⇒ 3 y = 12

⇒ y = 123

⇒ y = 4

Put in equation (1).

⇒ − x + 34 = 3

⇒ − x + 12 = 3

⇒ − x = 3 − 12

⇒ − x = − 9

⇒ x = 9

Since, number of students in class = xy.
Substitute x=9 and y=4 in above equation.
Number of students in class is,

= 9 × 4 = 36

Hence, the total number of students in the class is 36.
The correct option is (1).

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