Question

The students of a class are made to stand in rows. If 3 students are extra in a row, then 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 1

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

Assumption :-

Number of rows be t

Number of students in a row be p

Total students of the class = pt

Case (1) :-

Total no. of students = (t - 1)(p + 3)

So,

pt = (t - 1) (p + 3)

pt = pt - p + 3t - 3

3t - p - 3 = 0

3t - p = 3

-p + 3t = 3 ...... (1)

Case (2) :-

Total number of students = (t + 2)(p - 3)

pt = pt + 2p - 3t - 6

2p - 3t = 6 ..... (2)

Now,

Multiply (1) by 2 we get,

= 2[-p + 3t = 3]

= -2p + 6t = 6 ...... (3)

Now,

Adding (1) and (3) we get,

3t = 12

$\tt{\rightarrow t=\dfrac{12}{3}}$

t = 4

Substituting value of t in (1),

-p + 3t = 3

-p + 3(4) = 3

-p + 12 = 3

-p = 3 - 12

-p = - 9

p = 9

Students in class

= pt

= 9 × 4

= 36

Therefore,

Number of students in class = 36

Answer 2

$\huge\underline\mathrm{SOLUTION:-}$

AnswEr:

• The number of students in the class = 36.

Given:

• The students of a class are made to stand in rows. If 3 students are extra in a row, then there would be 1 row less. If 3 students are less in a row, there would be 2 rows more.

Need To Find:

• The number of students in the class = ?

ExPlanation:

Let the number of rows be x.

Number of students in 1 row = y

According to the given question:

➠ (y + 3) (x - 1) = xy

∴ xy + 3x - y - 3 = xy

Or:

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

➠ (y - 3) (x + 2) = xy

∴ xy - 3x + 2y - 6 = xy

Or:

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

Adding (1) and (2) We Get:

• y = 9

ThereFore:

➠ 3x - 9 = 3

➠ x = 4

ThereFore:

Number of students = xy = 4 × 9 = 36.

• Hence, the number of students is 36.

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