ANSWERS - HURDLE 22 : PROFIT AND LOSS (Quadratic Equations)

Ans 1. 961

Ans 2. 1764

Ans 3. 3481

Ans 4. 5041

Ans 5. 6561

Ans 6. 9025

Ans7. 529

Ans8. 5776

Ans 9. 2116

Ans 10. 9216

Ans 11. 2916

Ans12. 484

Ans13. 4761

Ans14. 100

Ans15. 900

Ans16. 1225

Ans17. 1225

Ans18. 2500

Ans19. 225

Ans20. 225

Ans21. 400

Ans22. 900

Ans23. 400

Ans24. C , Ans25. E , Ans26. F , Ans27. H , Ans28. J , Ans29. K , Ans30. L

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HERE ARE SOLUTIONS OF SOME OF THE QUESTIONS, THE REST MAY BE SOLVED USING THE SAME METHOD.

Solution1. X*(100+X)/100= 39
or X^2 +100X-3900=0
X^2 +130X-30X-3900=0
Solving (X-30)(X+130)=0
So x= 30 or -130. As negative is not possible X=30.
So cost price of X+1 items each purchased for X+1 = 31*31= 961.

Solution8. X*(100-X-1)/100=18
=> X*(99-X)=1800
=> X^2-99X+1800=0
=> X^2 -75X-24X+1800 =0
=> X(X-75) -24(X-75)=0
So X= 24 or 75, as X>50, X is 75.
(X+1)*(X+1)= 5,776

Solution10. X*(100+X+2)/100 = 196
=> X*(102 +X) = 19600
=> X^2 + 102X - 19600 = 0
=> X^2 + 200X-98X- 19600=0
so X(X+200) -98(X+200)
(X-98 )(X+200) =0
So X = 98 as X cannot be negative.
(X-2) * (X-2) = 9216


Solution11. X*(100-X+2)/100 = 26
X*(102-X) = 2600
X^2-102X+2600 = 0
X^2- 52X-50X +2600 = 0
X= 50 or 52
As X is greater than 50 it can be 52 only
SO answer is 2916 .

Solution12 . X*(100+X+3)/100 = 32
X(103 +X) = 3200
X^2+ 103X = 3200
X^2+ 128X-25X -3200= 0
so X = 25 and Ans is 484

Solution22. X*(100-X-15)/100 = 18
X*(85-X) = 1800
X^2- 85X +1800 = 0
X^2- 40X-45X +1800 =0
so X = 40 or 45
as X is greater than 40 it can be 45 only.
So answers is 900