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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?

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? Correct Answer 48

Given:

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

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

Calculation:

Let the total number of students be x.

According to the question, (x/4) = Number of benches needed for all the students

When 4 students sit on one bench, number of benches left = 3

Then, according to the first condition, the total number of benches = (x/4) + 3      ----(1)

 According to the question, (x/3) = number of benches needed for all - 1

When 3 students sit on one bench, number of benches needed extra = 1

Then, according to the second condition, the total number of benches available = (x/3) - 1      ----(2)

Equating (1) and (2),

(x/3) - 1 = (x/4) + 3

⇒ (x/12) = 4 

⇒ x = 48

∴ The total number of students present in the class is 48.

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