A) 50
B) 60
C) 45
D) 55
Correct Answer: A
Solution :
Let x be the number of persons and y be the amount received by each person. According to the question,\[xy=6500~\] ...(1) Also, \[(x+15)\,(y-30)=6500\] ...(2) \[\Rightarrow \] \[xy-30x+15y-450=6500\] \[\Rightarrow \]\[6500-30x+15y-450=6500\] [From (1)] \[\Rightarrow \] \[2x-y+30=0\] \[\Rightarrow \] \[2x-\frac{6500}{x}+30=0\] [From (1)] \[\Rightarrow \] \[2{{x}^{2}}-6500+30x=0\] \[\Rightarrow \] \[{{x}^{2}}+15x-3250=0\] \[\Rightarrow \] \[(x-50)\,(x+65)=0\] \[\Rightarrow \] \[x=50\] or \[x=-65\] Since, number of persons cannot be negative. Hence, number of persons = 50
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