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Mathematics

The students of a class are made to stand in (complete) rows. If one student is extra in a row, there would be 2 rows less, and if one student is less in a row, there would be 3 rows more. Find the number of students in the class.

Linear Equations

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Answer

Let number of students in a row be x and no. of rows be y.

Total no. of students = xy.

According to first condition we have,

⇒ (x + 1)(y - 2) = xy

⇒ xy - 2x + y - 2 = xy

⇒ xy - xy + y - 2x = 2

⇒ y - 2x = 2 ………(i)

According to second condition,

⇒ (x - 1)(y + 3) = xy

⇒ xy + 3x - y - 3 = xy

⇒ 3x - y = 3 + xy - xy

⇒ 3x - y = 3 ……..(ii)

Adding (i) and (ii) we get,

⇒ (y - 2x) + (3x - y) = 2 + 3

⇒ y - y - 2x + 3x = 5

⇒ x = 5.

Substituting value of x in (i) we get,

⇒ y - 2(5) = 2

⇒ y - 10 = 2

⇒ y = 12.

xy = 5 × 12 = 60.

Hence, there are 60 students in the class.

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