Question

In the morning batch at ‘school’ we have observed that when five students took seat on each bench, 4 students remain unseated. But when eleven students took seat per bench, 4 benches remain vacant. The number of students in the morning batch were?
 \[\begin{align}
  & (A)56 \\
 & (B)48 \\
 & (C)26 \\
 & (D)44 \\
\end{align}\]

Answer 1

Hint: We have to assume the number of benches in the classroom as x and the number of students in the classroom as y. From the question, it was given that five students took seats on each bench, 4 students remained unseated. Now write this equation in terms of x and y. Assume this equation as equation (1). From the question, it was also given that when eleven students took seats per bench, 4 benches remained vacant. Now we have to write this equation in terms of x and y. Assume this equation as equation (2). Now by subtracting equation (1) with equation we get the value of x. Now by placing x in equation (1), we get the value of y. The obtained value of y represents the number of students in the morning class.

Complete step by step solution:
In the question, it was given that when five students took seats on each bench, 4 students remained unseated but when eleven students took seats per bench, 4 benches remained vacant.
Let us assume the number of benches in the classroom as x and the number of students in the classroom as y.
We know that when five students took seats on each bench, 4 students remained unseated.
We get
\[y=5x+4.....(1)\]
We also know that when eleven students took seats per bench, 4 benches remained vacant. Here, the number of benches sufficient for all the students are (x-4).
We get
\[y=11(x-4).....(2)\]
Now we will substitute equation (2) in equation (1).
\[\begin{align}
  & \Rightarrow 11(x-4)=5x+4 \\
 & \Rightarrow 11x-44=5x+4 \\
 & \Rightarrow 11x-5x=44+4 \\
 & \Rightarrow 6x=48 \\
 & \Rightarrow x=8.....(3) \\
\end{align}\]
Now we will substitute equation (3) in equation (2).
\[\begin{align}
  & \Rightarrow y=11(8-4) \\
 & \Rightarrow y=11(4) \\
 & \Rightarrow y=44...(4) \\
\end{align}\]
From equation (3) and equation (4), it is clear that the number of benches is equal to 8 and number of students are equal to 44.
Hence, option (D) is correct.

Note: We should be careful while applying the assumptions into the question. So many students may confuse how the equation (2) is written. We know that the number of benches equal to x. In the question, it was mentioned that if 11 students sit in one bench then 4 benches are left vacant. So, the number of benches required for all the students are (x-4). So, we have equated y with the product of 11 and (x-4). Students should have a clear view at this point to solve this problem. There is a possibility that students might take it as 11x-4 and can go wrong hence.