Multiple choice

Out of 36 students in a hostel, 19 leave. Due to this, the mess expenses come down by \$48 per day, but the average expense per head increases by \$5. What is the new expenditure per day of the mess?

  1. $252
  2. $204
  3. $300
  4. $240

  5. Cannot be determined
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let original average be x and total students be 36. Total expense = 36x. After 19 leave, 17 remain. New total expense = 36x - 48. New average = (36x - 48) / 17. Given (36x - 48) / 17 = x + 5. Solving for x: 36x - 48 = 17x + 85 => 19x = 133 => x = 7. New expenditure = 36(7) - 48 = 252 - 48 = 204.

AI explanation

Let the initial average expense be x. The initial total expenditure is 36x, and the new total expenditure is 17 multiplied by (x plus 5). The problem states the daily expenses come down by 48, so 36x minus 17x minus 85 equals 48. Solving 19x equals 133 gives an initial average of 7. The new expenditure per day is 17 multiplied by 12, which equals 204.

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