Question

Maths Puzzle Question !?  Q1. Of 28 students taking atleast one of Mathematics, English or History, those students taking only one subject are all taking Mathematics. Of those students taking exactly two of the three subjects, it is known that the number taking Mathematics and English is identical to the number taking Mathematics only. Six students are taking Mathematics and History only and the number taking History and English is even, non-zero and equal to 5 times the number taking all three subjects. Find the number of students taking Mathematics and English only. 

Q2. A wizard having powers of mystic in conditions and magical medicines, seeing a dog fight [not of airplains :P] going on, spoke privately to both the owners of dogs. To one she said, "If your dog wins, then you give me your stake money, but if you do not win, I shall give you two-thirds of that." Going to the other, he promised in the same way to given three-fourths. From both of them, his gain would be only 12 gold coins. Find the stake of money each of the dog-owners have.

Answer 1

puzzle 1 .

total number of students = 28.
maths and history taken by 6 students .

therefore remaining studensts = 28 - 6
                  = 22.

students taking history and english are even and non-zero and are equal to five times the students taking history , english and mathematics.

therefore,
 students with history and english = 2 (IT cannot be 4 since 4 + 5*4 IS > 22(the number of remaining students) )
 students with history , english , maths = 5*2
                    = 10

In case of Number of history and english students =2 ,the number of mathematics students = (22 - 2- 5*2 )/2
                         = (22 - 2 -10)
                        = 5
Note the division is because number of students    with maths only = number of students taking maths and english .