There were 35 students in a hostel. If the number of students

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There were 35 students in a hostel. If the number of students increased by 7, the expenses of the mess were increase by Rs 42 per Day , while the average expenditure per head diminished by Re. 1 The original expenditure of the mess was ?

1. Rs. 40
2. Rs . 420
3. Rs . 432
4. Rs . 442

Correct Option: B

Let the original expenditure be Rs. y per day ,
Then, y / 35 - [( y + 42 ) / 42 ] = 1
⇒ 42y - 35 ( y + 42 ) = 35 x 42
∴ 7y = 35 x 42 + 35 x 42
⇒ y = ( 2 x 35 x 42 ) / 7
= 420
Hence , the original expenditure is Rs . 420