Question

Symbiosis runs a corporate training programme. At the end of the first programme, the total takings were ₹38950. There were more than 45 but fewer than 100 participants. What was the participants' fee?

• A. ₹410
• B. ₹450
• C. ₹500
• D. ₹510

Hint:

When total revenue and an admissible headcount range are given, check which fee option exactly divides the total and yields a participant count in the required interval.

Answer 1

The Correct Option is A

Step 1: Convert the statement into an equation.
Let the fee be $f$ and the number of participants be $p$. Then \[ fp = 38950,\qquad 46 \le p \le 99,\qquad p\in\mathbb{Z}. \] Step 2: Test the options (must divide 38950 and yield $p$ in range).
\[ p=\frac{38950}{f}. \] For $f=₹410$: $p=\dfrac{38950}{410}=95$ (integer, and $46\le 95\le 99$)\ ⇒\ \text{valid}.
For $f=₹450$: $p=\dfrac{38950}{450}\notin\mathbb{Z}$\ ⇒\ \text{invalid}.
For $f=₹500$: $p=\dfrac{38950}{500}=77.9\notin\mathbb{Z}$\ ⇒\ \text{invalid}.
For $f=₹510$: $p=\dfrac{38950}{510}\notin\mathbb{Z}$\ ⇒\ \text{invalid}.
Step 3: Conclude.
Only $f=₹410$ gives an integer participant count within the required range. \[ \boxed{\text{Participants' fee }=\ ₹410} \]