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There were 42 students in a hostel. If the number of students is increased by 7 the expenditure on food increases by 49 per day while the average expenditure is reduced by Re 1. What was the initial expenditure on food per day? 
  • a)
    420 
  • b)
    540 
  • c)
    580 
  • d)
    588 
Correct answer is option 'D'. Can you explain this answer?
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There were 42 students in a hostel. If the number of students is incre...
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Given information:
- Initially, there were 42 students in a hostel.
- If the number of students is increased by 7, the expenditure on food increases by 49 per day.
- The average expenditure is reduced by Re 1.

To find: The initial expenditure on food per day.

Let the initial expenditure on food per student per day be x.

Total expenditure on food per day initially = 42x

When the number of students is increased by 7, the total number of students becomes 42+7 = 49.

Let the increased expenditure on food per student per day be y.

Total expenditure on food per day after the increase in the number of students = 49y

According to the given information, we have:

49y - 42x = 49 .....(1) (As the expenditure on food increases by 49 per day)

Also, we know that the average expenditure is reduced by Re 1.

So, we have:

(49y)/(49) - (42x)/(42) = x-1

y-x = 1 .....(2)

Solving equations (1) and (2), we get:

x = 588

Therefore, the initial expenditure on food per day was Rs. 588.
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There were 42 students in a hostel. If the number of students is increased by 7 the expenditure on food increases by 49 per day while the average expenditure is reduced by Re 1. What was the initial expenditure on food per day?a)420b)540c)580d)588Correct answer is option 'D'. Can you explain this answer?
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