Question

14. In a town of 10,000 families, it was found that 40% of the families buy newspaper A, 20% buy newspaper B, 10% buy newspaper C,5% buy A and B;3% buy B and C and 4% buy A and C. If 2% buy all the three newspapers, find the number of families which buy
(i) A only,
(ii) B only,
(iii) none of A, B and C.


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Answer 1

Answer:

Let ;-

A = ( 1 , -1 , 3)

B = ( 2 , -4 , 5)

C = ( 5 , -13, 11)

If , all these points lie on the straight lines than ;-

=> AC = AB + BC

=> AB = √( 2-1 )² + ( -4 + 1)² +( 5-3 )²

=> AB = √ 1 + 9 + 4

=> AB = √ 14

=> AB = 2√5

=> BC = √ ( 5 - 2 )² + ( - 13 + 4 )² + ( 11 - 5 )²

=> BC = √ 9 + 81 + 36 = 3 √ 14

=> AC = √ ( 5 - 1 )² + ( - 13 + 1 )² + ( 11 - 3 )²

=> AC = √ 16 + 144 + 64

=> AC = 4 √ 14

=> AB + BC = AC

=> L. H. S = √ 14 + 3√ 14

=> L. H. S. = 4 √ 14 = AC

=> L. H. S. = R. H. S.

Therefore,

The given points are in a Straight line.

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