Question : A group of college students had decided to complete a project in 10 days. As 2 students dropped out every day, the project was completed at the end of the 15th day. The number of students at the beginning of the project was:
Option 1: 42
Option 2: 40
Option 3: 35
Option 4: 45
Correct Answer: 42
Solution :
$ND = N{_1}D{_1} + N{_2}D{_2} +N{_3}D{_3} +......+N{_n}D{_n} $, where $N$ = number of students and $D$ = number of days.
Let the number of students be $x$ initially.
$10x = x\times 1 + (x-2)\times1+(x-4)\times 1 + ......(x-28)\times1$
⇒ $10x=15x -[2+4+6+....+28]$
⇒ $5x = \frac{14}{2}[2 + 28]$
⇒ $5x=7\times30$
$\therefore x=42$
Hence, the correct answer is 42.
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