Question

There were 46 students in a Boys hostel. Due to
the admission of eight new students the
expenses of the hostel mess were increased by
Rs.42 per day while the average expenditure per
head diminished by Rs 1. What was the original
expenditure of the hostel mess?​

Answer 1

$\large \frak \green{ \pmb{ \underline{Given :}}}$

• There were 46 students in a Boys hostel.

• Due to the admission of eight new students the expenses of the hostel mess were increased by Rs.42 per day

• while the average expenditure per head diminished by Rs 1.

$\large \frak \green{ \pmb{ \underline{To \: find :}}}$

• What was the original
• expenditure of the hostel mess?

$\large \frak \green{ \pmb{ \underline{ Solution:}}}$

$\sf{let \: x = average \: daily \: expense \: per \: head.}$

$\sf{This \: becomes \: x-1 \: when \: 8 \: students \: are \: added}$

$\sf{Then \: original \: expence = 46x}$

$\sf{Expense \: after \: 8 \: students \: added = 54( \times - 1)}$

$\sf{We \: are \: given,}$

$\sf{54(x - 1) = 46x + 42}$

$\sf{ solving \: for \: x}$

$\sf{ \qquad : \implies \: 54x - 54 = 46x + 42}$

$\sf{ \qquad : \implies \: 54x - 46x = 42 + 54}$

$\sf{ \qquad : \implies \: 8x = 96}$

$\sf{ \qquad : \implies \: x = \cancel {\frac{96}{8} }}$

$\sf \qquad : \implies {\underline \pink{ \: x = 12}}$

______________________________________

$\sf{we \: need \: to \: find \: original \: expense = 46x = 46 \times 12 = 552}$

$\sf \therefore{ \underline \orange{ The \: original \: expense \: of \: the \: hostel \: mess \: is \: 552 \: ruppe}}$