Question

A natural no., when increased by 12 equals 160 times its reciprocal. Find the no.

Answer 1

Dear student,

Following is the answer to your query:

Let the number be n.

According to the given condition the equation formed will be:
n+12 = $\frac{160}{n}$
$$\begin{gathered} \Rightarrow n^2+12n-160=0 \\ \Rightarrow n^2+20n-8n-160=0 \\ \Rightarrow n(n+20)-8(n+20)=0 \\ \Rightarrow n=8,-20 \end{gathered}$$
Since, n is a natural so n cannot be -20
Hence, n=8