question_answer

Twenty one times of a positive number is less than its square by 100. The value of the positive Number is [SSC CGL Tier II, 2017]

A) 25

B) 26

C) 42

D) 41

Correct Answer: A

Solution :

[a] Let, positive number \[=x\] According to the question,             \[x\times 21={{x}^{2}}-100\] \[\Rightarrow \]   \[{{x}^{2}}-21x-100=0\] \[\Rightarrow \]   \[{{x}^{2}}-25x+4x-100=0\] \[\Rightarrow \]   \[x\,\,(x-25)+4\,\,(x-25)=0\] \[\Rightarrow \]   \[(x-25)(x+4)=0\] \[\Rightarrow \] \[x=25,\]\[-\,\,4\] Since number is positive \[\therefore \]