Question

There are some benches in the classroom. If $4$students sit on each bench, then $3$ benches are left unoccupied. However, if $3$ students sit on each bench, $3$ students are left standing. How many students are there in the class?

• A. $52$
• B. $36$
• C. $24$
• D. $48$

Answer 1

The correct option is D

$48$

Step-1: Given Information

Let there is $n$number of students in the class.

Total number of benches in the class, If $4$students sit on each bench = $\frac{n}{4}+3$ ( As $3$ benches are left unoccupied )

Total number of benches in the class, If $3$students sit on each bench = $\frac{n}{3}-\frac{3}{3}$$=\frac{n}{3}-1$( As $3$ students are left standing and $3$ students sit on each bench )

Step-2: Find the number of students $n$in the class

$\frac{n}{4}+3$$=\frac{n}{3}-1$ ( As the number of benches in a class will be the same )

$3+1=\frac{n}{3}-\frac{n}{4}$( Transpose the constant term on one side and variable on the other side )

$4=\frac{4n-3n}{12}$

$12\times 4=n$

$48=n$

Or, $n=48$

Hence, the number of students in the class is $48$

Hence, the option $D$ is correct.