# 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:**

Let us assume the number of rows equal to x and the number of students in each row be y. Then the total number of students in the class can be calculated by;

total number of students = number of rows × number of students in each row

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

Then the number of students in the class be 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 + 2 y - 6 = xy

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

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

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

**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:

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

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, number of students in the class are 36