(Q.41).In X class, if three students sit on each bench, one student will be left. If four students sit on each bench, one bench will be left. Find the number of students and the number of benches in that class.

Let the number of benches = x say and the number of students = y

By problem

y = x + ⇒ x – y + = 0

and y = (x – ) ⇒ x – y – = 0

3x - y = -1
x y (x,y)
0 (0,)
1 (1,)
4x - y = 4
x y (x,y)
0 - (0,-)
1 (1,)

The two lines intersect at (, ).

∴ The solution of the equation is x = and y =

i.e., Number of benches = and the number of students =