In a hostel of $50$ students, food provisions last $40$ days. If after $10$ days, $30$ more students join,…

In a hostel of $50$ students, food provisions last $40$ days. If after $10$ days, $30$ more students join, the remaining food will now last:
  1. $15$ days
  2. $\dfrac{75}{4}$ days
  3. $20$ days
  4. $24$ days

Solution

After $10$ days, food left $= 50 \times (40 - 10) = 1500$ student-days. Now there are $80$ students, so it lasts $\dfrac{1500}{80} = \dfrac{75}{4} = 18.75$ days.

Asked in: IMO

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