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?

# 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?

1. A
425
2. B
410
3. C
420
4. D
430

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### Solution:

Let the average expenditure of 35 students be$\underline{x}$ After adding 7 new students, the average was decreased by 1 rupee.
The expenses of the mess were increased by 42 rupees.
Then,
Or, Expenses of 35 students = 35$\underline{x}$………(i)
After adding 7 new students, the average is
$\underline{x}$-1=……(ii)
Substituting (i) in (ii) we get,
$\underline{x}$-1=$\frac{35\underline{x}+42}{42}$
Or, 42$\underline{x}$−42=35xˉ+42
or, 7
$\underline{x}$=84
Or, $\underline{x}$=12 ----(iii)
substituting (iii) in (i) we get
expenses of 35 students=35$\underline{x}$=35×12=420
Therefore, the original expenditure of the mess is 420
Hence (3) is the correct option.

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