Question

There are certain benches in a classroom. If 4 students sit on each bench, three benches are left vacant and if 3 students sit on each bench, 3 students are left standing. What is the total number of students in the class?

Answer 1

Let the number of students be x and number of benches be y.
(i) When 4 students sit on one bench:
Number of benches occupied = y - 3
⇒ x = 4(y - 3)    ......(i)
(ii) When 3 students sit on one bench:
3 student are left standing
⇒ x = 3 = 3y
⇒ x = 3y + 3    ......(ii)
From (i) and (ii)
4(y - 3) = 3y + 3
4y - 12 = 3y + 3
y = 15
But x = 4(y - 3)     ...(from (i))
⇒ x = 4(15 - 3)
⇒ x = 48
Therefore, Number of students in the class = 48.