Q. 44.1( 146 Votes )

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.

Answer :

Let the number of rows be x and number of students in a row be y.

Total students of the class = Number of rows x Number of students in a row = xy

Using the information given in the question,

Condition 1

Total number of students = (x - 1) (y + 3)

= (x - 1) (y + 3)

= xy - y + 3x - 3

3x - y - 3 = 0

3x - y = 3 ....(i)

Condition 2

Total number of students = (x + 2) (y - 3)

= xy + 2y - 3x - 6

⇒3x - 2y = -6  ... (ii)

Subtracting equation (ii) from (i),

(3x - y) - (3x - 2y) = 3 - (-6)

⇒- y + 2y = 9

⇒3 + 6 y = 9

By using equation (i), we obtain 3x - 9 = 3,

⇒3x = 9 + 3

⇒3x = 12

⇒ x = 4

From (i),

⇒ 3(4) - y = 3

⇒ 12 - y = 3

⇒ 9 = y

Number of rows = x = 4

Number of students in a row = y = 9

Number of total students in a class = Number of students in 1 row × Number of rows

= xy

= 4 x 9

= 36

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Pair of Linear Equations in Two VariablesPair of Linear Equations in Two VariablesPair of Linear Equations in Two Variables46 mins
Dealing With the Real Life ProblemsDealing With the Real Life ProblemsDealing With the Real Life Problems53 mins
Learn to Solve Real Life Problems Using Linear Equations in Two VariablesLearn to Solve Real Life Problems Using Linear Equations in Two VariablesLearn to Solve Real Life Problems Using Linear Equations in Two Variables36 mins
Quiz | Real Life Problems Through Linear EquationsQuiz | Real Life Problems Through Linear EquationsQuiz | Real Life Problems Through Linear Equations56 mins
Quiz | Solution of Linear EquationsQuiz | Solution of Linear EquationsQuiz | Solution of Linear Equations53 mins
Champ Quiz | Consistency and Inconsistency of SolutionsChamp Quiz | Consistency and Inconsistency of SolutionsChamp Quiz | Consistency and Inconsistency of Solutions36 mins
Emphasizing on Elimination MethodEmphasizing on Elimination MethodEmphasizing on Elimination Method48 mins
Dealing with the Real Life ProblemsDealing with the Real Life ProblemsDealing with the Real Life Problems54 mins
Elimination (quicker than quickest)Elimination (quicker than quickest)Elimination (quicker than quickest)44 mins
Algebraic Methods to Solve Pair of Linear EquationAlgebraic Methods to Solve Pair of Linear EquationAlgebraic Methods to Solve Pair of Linear Equation44 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses