Question

Please please solve it

Answer 1

$\textsf{Let the Original Expenditure of the Mess be : M}\\\\\textsf{Given : The Original Number of Students in the Hostel = 48}$

$\sf{The\;Original\;Average\;Expenditure\;per\;head = \dfrac{Original\;Expenditure}{Total\;Number\;of\;Students}}$

$\sf{\implies The\;Original\;Average\;Expenditure\;per\;head = \dfrac{M}{48}}$

$\textsf{Given : The Number of Students are Increased by 9}$

$\sf{\implies The\;Present\;Number\;of\;Students\;in\;the\;Hostel : (48 + 9) = 57}$

$\textsf{Given : If the Number of Students are increased by 9, The expenses of the}\\\textsf{Mess were increased by Rs.42 per day}$

$\sf{\implies The\;New\;Expenditure\;of\;the\;Mess\;will\;be : M + 42}$

$\sf{\implies The\;New\;Average\;Expenditure\;per\;head = \dfrac{New\;Expenditure}{57}}$

$\sf{\implies The\;New\;Average\;Expenditure\;per\;head = \dfrac{M + 42}{57}}$

$\textsf{Given : The New Average Expenditure per head is 2 less than Original}\\\textsf{Expenditure per head}$

$\sf{\implies \dfrac{M + 42}{57} = \dfrac{M}{48} - 2}$

$\sf{\implies \dfrac{M + 42}{57} = \dfrac{M - 96}{48}}$

$\sf{\implies \dfrac{M + 42}{19} = \dfrac{M - 96}{16}}$

$\sf{\implies 16(M + 42) = 19(M - 96)}$

$\sf{\implies 16M + (16 \times 42) = 19M - (19 \times 96)}$

$\sf{\implies (19 \times 96) + (16 \times 42) = 19M - 16M}$

$\sf{\implies 3M = (19 \times 96) + (16 \times 42)}$

$\sf{\implies M = \dfrac{(19 \times 96)}{3} + \dfrac{(16 \times 42)}{3}}$

$\sf{\implies M = (19 \times 32) + (16 \times 14)}$

$\sf{\implies M = (608) + (224)}$

$\sf{\implies M = 832}$

$\sf{\implies The\;Original\;Expenditure\;of\;the\;Mess\;is\;Rs.832}$

Answer 2

answer is c ₹832
hope helped ✌✌✌