Question

A group of students of Ivy special high school were asked if they had siblings and/ or pets. Of the students who responded, 75% have siblings and 20% have pets. If 15% of the students who responded have neither siblings nor pets, what percent have both siblings and pets?

Answer 1

1. Check the picture

2. Let S denote the siblings set, P denote the pets set.

let the intersection of P and S be x%

S is in total 75%, so the part (partition) only P not S is (75-x)%
Similarly the part only S not P is (25-x)%

3. [(75-x)+x+(20-x)+15]=100%
       75-x+x+20-x+15=100
         110-x=100
               x=10


Answer : 10% of the students have both siblings and pets