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There were 35 students in a hostel. Due to the admission of 7 new students the expenses of  the  mess  were  increased  by  Rs.42  per  day  while  the  average  expenditure  per  head diminished by Re 1. What was the original expenditure of the mess?


Rs. 450


Rs. 320


Rs. 550


Rs. 420

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Option(D) is correct

Let the original average expenditure be Rs.$x$ then,

$42(x - 1) - 35x = 42$

$⇒ 7x = 84$

$⇒ x = 12$

Therefore original expenditure

$= Rs.(35 \times 12)$

$=\textbf{Rs. 420}$

Edit: For an alternative solution, check comment by Shreya.

Edit 2: For yet another alternative solution, check comment by Sravan Reddy.

(4) Comment(s)

Sravan Reddy

Simpler technique:

=> What would have been the additional expenses if the average did not fall by 1 rupee?

It will be 42 as there are 42 students. So additional expense by 7 was 42 (given in question) + 42(due to average) = 84.

So per person charge is $\dfrac{84}{7} = 12$.

So, initial charge is $35 \times 12 = 420$

P.S. Again this boils down to arithmetic equations but this is one way of thinking without involving equations so no paper needs to be used.


Kindly explain with easy method.


Sir, tell me how to solve this fully?


Let the original average expenditure per head be Rs. $x$ then,

$\textbf{Total expenditure}=\textbf{Number of students} \times$$ \textbf{Average Expenditure}$

So before 7 new students came (i.e. when there were 35 students in the hostel), total expenditure would be Rs. $35 \times x$

Now when 7 new students have come average expenditure has been reduced by rupee 1.

So average expenditure after 7 new students have come (so total students are $42$ now) Rs. $x-1$

And now total expenditure will become = Rs. $42\times (x-1)$

Now according to the question, due to the admission of 7 new students the expenses of the mess were increased by Rs. 42.

So, $42 \times (x - 1) - 35 \times x = 42$

or $7x = 84$

or $x=12$

So original total expenditure would have been,

\(35 \times x=35 \times 12= \textbf{Rs. 420}\)