# There are some benches in a 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?

$

{\text{A}}{\text{. 36}} \\

{\text{B}}{\text{. 48}} \\

{\text{C}}{\text{. 52}} \\

{\text{D}}{\text{. 56}} \\

{\text{E}}{\text{. 64}} \\

$

Answer

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Hint – Assume the number of students in the class be x so, when 4 students sit on each bench and 3 benches are left unoccupied so the number of benches should be $\left( {\dfrac{x}{4} + 3} \right)$ so, use this method to reach the answer.

Let, the number of students in the class = x

Now according to question

When 4 students sit on each bench, then 3 benches are left unoccupied.

Therefore the number of benches $ = \dfrac{x}{4} + 3$.

Now, 3 students sit on each bench, 3 students are left standing.

Therefore the number of benches $ = \dfrac{{x - 3}}{3}$.

Now both the above are equal so, equate them we have

$

\Rightarrow \dfrac{x}{4} + 3 = \dfrac{{x - 3}}{3} \\

\Rightarrow \dfrac{{x + 12}}{4} = \dfrac{{x - 3}}{3} \\

$

$

\Rightarrow 3x + 36 = 4x - 12 \\

\Rightarrow 4x - 3x = 36 + 12 \\

\Rightarrow x = 48 \\

$

Hence option (B) is correct.

Note – In such types of questions first convert the given conditions of the question into linear equations as above then equate these equations and simplify, we will get the required number of students in the classroom.

Let, the number of students in the class = x

Now according to question

When 4 students sit on each bench, then 3 benches are left unoccupied.

Therefore the number of benches $ = \dfrac{x}{4} + 3$.

Now, 3 students sit on each bench, 3 students are left standing.

Therefore the number of benches $ = \dfrac{{x - 3}}{3}$.

Now both the above are equal so, equate them we have

$

\Rightarrow \dfrac{x}{4} + 3 = \dfrac{{x - 3}}{3} \\

\Rightarrow \dfrac{{x + 12}}{4} = \dfrac{{x - 3}}{3} \\

$

$

\Rightarrow 3x + 36 = 4x - 12 \\

\Rightarrow 4x - 3x = 36 + 12 \\

\Rightarrow x = 48 \\

$

Hence option (B) is correct.

Note – In such types of questions first convert the given conditions of the question into linear equations as above then equate these equations and simplify, we will get the required number of students in the classroom.

Last updated date: 26th Sep 2023

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