Let the no of people that bought all the three products be ‘x’, and no of people that bought both pen and notebook be y . Then no of people that bought pencil only = 20 x And those who bought notebook only = 40 x Venn diagram according to question can be drawn as: Thus from the figure we get 40x + (19 -x) + x + y = 120 =) 40x + y = 101 Now if we take a close look at the equation we can conclude that the value x can be either ‘1’ or ‘2’ Putting x = 1 in the equation we get y =61. But we have to also meet the additional condition that 15- x, 19-x, y are in A.P. which is not possible in this case. Hence it is rejected. Thus the value of x = 2, hence we will get y = 21, which also satisfies the additional condition. Now if we see the figure again we can see that only pen can either be 0, 60, and 120 to satisfy the additional condition. And as it cannot be less than 50 (Specified in the question), the only value only pencil can take = 60 Thus 1) Total no of people that visited the shop = 60 + 13 + 2 + 40 + 17 + 80 + 21 = 233 2) The no people that bought both pen and notebook = 21 Correct Answer: 233, 21
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