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?

Solution

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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.

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