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

Solution:

We will be using the concept of two-variable linear equations to solve the given question.

Let us assume the number of rows to be equal to x and the number of students in each row to be y.

Then the total number of students in the class can be calculated as follows:

Total number of students = Number of rows × Number of students in each row = xy

Therefore, the number of students in the class is xy.

Using the information given in the question,

Condition 1: If 3 students are extra in a row, there would be 1 row less

(x - 1)(y + 3) = xy

xy + 3x - y - 3 = xy

3x - y = 3 ....(1)

Condition 2: If 3 students are less in a row, there would be 2 rows more

(x + 2)(y - 3) = xy

xy - 3x + 2y - 6 = xy

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

Adding equations (1) and (2), we obtain

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

y = 9

Substituting y = 9 in equation (1), we obtain

3x - 9 = 3

3x = 12

x = 4

Hence, number of students in the class, xy = 4 × 9 = 36

☛ Check: NCERT Solutions Class 10 Maths Chapter 3

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Video Solution:

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

Class 10 Maths NCERT Solutions Chapter 3 Exercise 3.7 Question 4

Summary:

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 fewer in a row, there would be 2 rows more. Hence, the number of students in the class is 36.

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