A number x is selected from first 100 natural numbers. Find the probability that x satisfies the condition x+100x>50
A
55100
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B
45100
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C
1
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D
50100
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Solution
The correct option is B55100 x+100x>50⟹x2+100>50x⟹x2−50x+100+(25)2−(25)2>0⟹x2+(25)2−50x−525>0⟹(x−25)2>525⟹x−25>±√525⟹x>25+22.91,x<25−22.91⟹x>47.91,x<2.09⟹x≥48,x≤2
As we have to select from 1 to 100 and x is greater than or equal to 48. Hence we have to select from 49 to 100 which is 53 numbers and favorable cases are 1, 2.