Akash on his birthday distributed on an average 10 toffees per student. If on the arrival of the teacher and the headmaster to whom Akash gave 15 and 20 toffees respectively, the average toffee distributed per head increases to 11.5, then what is the numb

Akash on his birthday distributed on an average 10 toffees per student. If on the arrival of the teacher and the headmaster to whom Akash gave 15 and 20 toffees respectively, the average toffee distributed per head increases to 11.5, then what is the number of students among whom the sweets were distributed?

Let’s assume that initial number of students be $x$.

∴ number of toffees given to x students $= 10x$

After the arrival of teacher and headmaster, total toffees distributed $= 10x + 15 + 20 = 10x + 35$

Now, the average becomes 1$1.5,$

∴ $10x + 35 = 11.5 × (x + 2)$

⇒ $10x + 35 = 11.5 x + 23$

⇒ $x = 8$

∴ the number of students among whom the sweets were distributed is $8$.

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