# The product of the ages of Ankit and Nikita is 240. If twice the age of Nikita is more than Ankit’s age by 4 years, what is Nikita’s age ?

$\par&space;Let&space;Ankit's&space;age&space;be&space;x&space;years.&space;Then,&space;Nikita's&space;age&space;=$  $\frac{240}{x}&space;years.$

$2&space;\times&space;\frac{240}{x}&space;-&space;x&space;=&space;4$

$480&space;-&space;x^{2}&space;=&space;4x$

$x^{2}&space;+&space;4x&space;-&space;480&space;=&space;0$

$(x&space;+&space;24)&space;(x&space;-&space;20)&space;=&space;0$

$x&space;=&space;20$

$\par&space;Hence,&space;Nikita's&space;age&space;=$ $(\frac{240}{20})$  $\par&space;years&space;=&space;12&space;years$