How do you calculate it?

Question

A factory manufactures products in two grades of quality. 90% of its revenues comes from manufacturing the first-rate product. How will the revenues change if production of the first-rate product is increased by 10% while the production of second-rate product is decreased by 10%?

Answer 1

$$90\%\cdot r=r_1\implies10\%\cdot r=r_2$$

$$r'=110\%\cdot r_1+90\%\cdot r_2=(110\%\cdot90\%+90\%\cdot10\%)\cdot r$$

Answer 2

HINT

Say current total amount is $m$. Let $x$ for first-rate product, $y$ for the rest.

Step 1: could you show what $x,y$ are in terms of $m$?

Step 2: what is $x$ increasing by $10\%$, and what is $y$ decreasing by $10\%$?

Step 3: what is the new total amount in terms of $m$, and could you find the new percentage now?