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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 Rs. 1. What was the original expenditure of the mess?

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425

410

420

430

answer is C.

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Detailed Solution

Let the average expenditure of 35 students be

\underset{̲}{x}

After adding 7 new students, the average was decreased by 1 rupee.
The expenses of the mess were increased by 42 rupees.
Then,

\underset{̲}{x} = \frac{expenses of 35 students}{35}

Or, Expenses of 35 students = 35

\underset{̲}{x}

………(i)
After adding 7 new students, the average is

\underset{̲}{x}

-1=

\frac{Expenses of 35 students + 42}{35 + 7}

……(ii)
Substituting (i) in (ii) we get,

\underset{̲}{x}

-1=

\frac{35 \underset{̲}{x} + 42}{42}

Or, 42

\underset{̲}{x}

−42=35xˉ+42
or, 7

\underset{̲}{x}

=84
Or,

\underset{̲}{x}

=12 ----(iii)
substituting (iii) in (i) we get
expenses of 35 students=35

\underset{̲}{x}

=35×12=420
Therefore, the original expenditure of the mess is 420
Hence (3) is the correct option.

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