Question
There are certain benches in a classroom. If $4$ students sit on each bench, three benches are left vacant and if $3$ students sit on each bench, $3$ students are left standing. What is the total number of students in the class?
✓
Answer
Let the number of students be $x$ and number of benches be $y.$
$(i)$ When $4$ students sit on one bench:
Number of benches occupied $= y - 3$
$\Rightarrow x = 4(y - 3) \dots......(i)$
$(ii)$When $3$ students sit on one bench:
$3$ student are left standing
$\Rightarrow x = 3 = 3y$
$\Rightarrow x = 3y + 3 \dots......(ii)$
From $(i)$ and $(ii)$
$4(y - 3) = 3y + 3$
$4y - 12 = 3y + 3$
$y = 15$
But $x = 4(y - 3) \dots...($from $(i))$
$\Rightarrow x = 4(15 - 3)$
$\Rightarrow x = 48$
Therefore, Number of students in the class $= 48.$
$(i)$ When $4$ students sit on one bench:
Number of benches occupied $= y - 3$
$\Rightarrow x = 4(y - 3) \dots......(i)$
$(ii)$When $3$ students sit on one bench:
$3$ student are left standing
$\Rightarrow x = 3 = 3y$
$\Rightarrow x = 3y + 3 \dots......(ii)$
From $(i)$ and $(ii)$
$4(y - 3) = 3y + 3$
$4y - 12 = 3y + 3$
$y = 15$
But $x = 4(y - 3) \dots...($from $(i))$
$\Rightarrow x = 4(15 - 3)$
$\Rightarrow x = 48$
Therefore, Number of students in the class $= 48.$
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