Question

Find a natural number whose square when decreased by 84 is equal to 24 more than thrice the given number.

• A. 11
• B. 15
• C. 12
• D. 14

Answer 1

The correct option is C

12

Let n be a required natural number.
Square of a natural number diminished by 84 = $n^2-84$
24 more than thrice the given number = 3n + 24
Now, by given condition,
$\Rightarrow n^2-84=3n+24\Rightarrow n^2-3n-108=0\Rightarrow n^2-12n+9n-108=0$ [by splitting the middile term]
$\Rightarrow n(n-12)+9(n-12)=0\Rightarrow (n-12)(n+9)=0\Rightarrow n=12$ $[\because n\ne$ -9 because n is a natural nember $]$
Hence, the required natural number is 12.