Question

In the morning batch at 'a school' we have observed that when five students took seat on eachbench, 4 students remained unseated. But when eleven students took seat per bench, 4 benches remained vacant. The number of students in the morning batch were?

• A. 55
• B. 48
• C. 26
• D. 44

Answer 1

The correct option is D 44

Student & branch

$\to$ let $x$ equal the number of benches

let y equal the number of students

when these are 5 students to a bench 4 student

remain

$y-4=5x...\left(i\right)$

when these are 11 student to a bench then 4 benches

remain

$\therefore y=11x-\mathrm{44...}\left(ii\right)$

$\to$ solving equation (i) & (ii)

$5x+4=11x-44$

$\therefore 4+44=11x-5x$

$\therefore 48=6x$

$\therefore x=8$

$\to$ put, $x=8$ in equation (i)

$y=5x+4$

$=5\left(8\right)+4$

$y=44$

$\to 8$ benches and $44$ students in class.