Question 42

There are some benches and some students in a classroom. If one student sits on one bench, 10 students will be left without a bench. If two students sit on a bench, 10 benches will have no students sitting on them. What is the ratio of students and benches in the class room?

Name: There are some benches and some students in a classroom. If one student sits on one bench, 10 students will be left without a bench. If two students sit on a bench, 10 benches will have no students sitting on them. What is the ratio of students and benches in the class room?
Uploaded: 2025-07-16T13:19:28.559664+05:30
Duration: 1 min 55 s
Description: There are some benches and some students in a classroom. If one student sits on one bench, 10 students will be left without a bench. If two students sit on a bench, 10 benches will have no students sitting on them. What is the ratio of students and benches in the class room?

Solution

Let the number of benches be 'b' and number of students be 's'
From first statement,
b(1) + 10 = s
b + 10 = s ....... (i)
From second statement,
Let us consider x benches are occupied with two students, i.e.
x(2) + (b-x)0 = s
2x = s ......... (ii)
It is given,
b - x = 10 ......... (iii)
Solving (i), (ii) and (iii), we get
x = 20, b = 30 and s = 40
students:benches = 40:30 = 4:3

Answer is option D.