Question

There are some benches in the class room having the number of rows 4 more than the number of columns. If each bench is seated with 5 students, there are two seats vacant in the class of 158 students The number of rows is ​

Answer 1

Given:

Total number of students - 158

Each bench contains- 5 students

Let-

No. Of columns=x

No. Of rows = x+4

Therefore number of benches are = x(x+4)

Therfore, Total number of students will be= 5*x(x+4). (1)

Acc to ques, equation 1 must be equal to 158

Therefore,

5*x(x+4) = 158 + 2

5*x(x+4) = 160

X(x+4) = 160/5

X² +4x = 32

X² +4x - 32 = 0

Here x can be calculated by splitting the middle term method.

(X-8)(x+4)=0

X=8 or x= -4

We know that value for x can't be negative

Therefore x = 8

Means no. Of columns= 8

And no. Of rows =8+4 = 12

Hence number of rows are 12