A manufacturer can sell $x$ items at a price of ₹$3x+5$ each. The cost price of $x$ items is ₹$x^2+5x$. If x is the number of items she should sell to get no profit and no loss, then:

$x=0$

$SP(x)=(3x+5)$ (Price function) selling as per each item $3x+5$ is S.P.

Cost price function $CP(x)=x^2+5x$

Profit(x) = $SP(x)-CP(x)$ for profit = 0

$SP(x)=CP(x)$

$⇒x(3x+5)=x^2+5x$

$⇒3x^2+5x=x^2+5x$

so, $3x^2=x^2⇒x=0$