Question

In a hostel of 100 students capacity, 42 are science graduate, 34 are law graduate and 58 are commerce graduate. 8 students are science and law graduate, 13 students are law and commerce graduate, 18 students are commerce and science graduate. How many students are only science graduate? ___

Answer 1

$\alpha +\beta +\gamma =100\alpha +2\beta +3\gamma =42+34+58=134\beta +3\gamma =8+13+18=39\alpha +\beta =(\alpha +2\beta +3\gamma )-(\beta +3\gamma )=134-39=95\therefore \gamma =(\alpha +\beta +\gamma )-(\alpha +\beta )\Rightarrow \gamma =100-95=5$
$\therefore$ Number of students who are only science graduate
= 42 - [(18 + 8 ) - 5]
= 42 - (13 + 3 + 5) = 21