In a classroom, there are certain number of benches. If 6 students are made to sit on a bench, then to accommodate all of them, one more bench is needed. However, if 7 students are made to sit on a bench, then after accommodating all of them, space for 5 students is left. What is the total number of students in the class?
(a)30
(b)42
(c)72
(d)None of these
Answer
Answer (as printed): C
Explanation
Let the number of benches in the class be $x$. Then, $6(x+1)=7 x-5 \Leftrightarrow x=11$. Hence, number of students in the class $$=6(x+1)=6 \times 12=72 .$$
Explanation as extracted from the printed page; notation may be imperfect.