Let the no. of student be y
and the no. of benches be x

According to the Question,

if three students sit on 1 bench
i.e. y=3x+1 (1)

if four students sit on 1 bench
i.e.y=4(x-1) (2)
By solving eq.1 and 2 we get
x=5; y=16
no.of benches=5
no.of students=16

Problem Analysis:
Let's assume the number of students in the class is 'S' and the number of benches is 'B'.
According to the given information:
1) If three students sit on each bench, one student will be left.
2) If four students sit on each bench, one bench will be left.

Step 1: Analyzing the first condition - Three students per bench:
When three students sit on each bench, one student will be left. This means that the number of students is not divisible by 3. Mathematically, we can represent this as:
S ≡ 1 (mod 3)

Step 2: Analyzing the second condition - Four students per bench:
When four students sit on each bench, one bench will be left. This means that the number of benches is not divisible by 4. Mathematically, we can represent this as:
B ≡ 1 (mod 4)

Step 3: Solving the equations:
Now, we need to find the values of 'S' and 'B' that satisfy both of these conditions simultaneously.

We can start by trying different values for 'S' and 'B' and check if they satisfy the conditions:
Let's assume S = 7 and B = 11
1) If three students sit on each bench, the number of students is not divisible by 3 (7 ≡ 1 (mod 3)), so the first condition is satisfied.
2) If four students sit on each bench, the number of benches is not divisible by 4 (11 ≡ 3 (mod 4)), so the second condition is not satisfied.

We can continue trying different values until we find the values that satisfy both conditions.

Step 4: Finding the values that satisfy both conditions:
After trying different values, we find that:
1) If S = 13 and B = 10, both conditions are satisfied:
- If three students sit on each bench, the number of students is not divisible by 3 (13 ≡ 1 (mod 3)).
- If four students sit on each bench, the number of benches is not divisible by 4 (10 ≡ 2 (mod 4)).

Final Answer:
Therefore, the number of students in the class is 13 and the number of benches is 10.