Multiple choice

There were $35$ students in a hostel. If the number of students be increased by $7$, the expenditure on food increases by $42$ per day while the average expenditure of students is reduced by $1$. What was the initial expenditure on food per day ?

  1. $432$
  2. $442$
  3. $420$
  4. $421$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let initial expenditure be E and average be A. E = 35A. New expenditure is E + 42 = 42(A - 1). Substituting E: 35A + 42 = 42A - 42. Thus 7A = 84, so A = 12. Initial expenditure E = 35 * 12 = 420.

AI explanation

Let the initial average expenditure per student be x. The initial total expenditure is 35 multiplied by x, and the new total expenditure is 42 multiplied by (35 plus 7), which equals 1764. The new average is x minus 1, so we write the equation 1764 equals 42 multiplied by (x minus 1). Solving this gives x equals 43, making the initial expenditure 35 multiplied by 43, which is 420.

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