A box contains either blue or red flags. The total number of flags in the box is an even number. A group of children are asked to pick up two flags each. If all the flags are used up in the process such that 60% of the children have blue flags, and 70% have red flags, what percentage of children have flags of both the colors?
Answers:  A) 5%  B) 10%  C) 15%  D) 20%  E) 30%
Solution: let the total number of flags be 100(even number)   let the total number of 'blue' flags alone be 'a'   let the total number of 'red' flags alone be 'b'   let the total number of 'both' flags be 'c'   We have given,   total number of blue flags = 60% = 60 = a+c   total number of red flags=70%=70=b+c   total number of flags = a+b+c=100 (since all the flags have been utilized)   So, substituting for c in the third equation, we have,   60-c+c+70-c=100   c=30   Option 30%.
<result>E</result>
A box contains either blue or red flags. The total number of flags in the box is an even number. A group of children are asked to pick up two flags each. If all the flags are used up in the process such that 60% of the children have blue flags, and 70% have red flags, what percentage of children have flags of both the colors?