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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