# Elementary question on percentages

In an economy, there are only two industries, mining and manufacturing. And it has been observed that a 10% rise in mining and a 20% rise in manufacturing can benefit the economy by 18% , but in a year, if the manufacturing industry as risen by 10%, and the economy has still risen by 18%, how much rise should have been observed in the mining industry.

My approach: ($E$- Economy, $M$- Mining, $F$- Manufacturing)

$E= M+F$ - (1)

$1.18E= 1.1M+1.2F$ - (2)

$1.18E= xM+ 1.1F$ -(3)

However, this is not very plausible. How should I go further.

Substituting $(1)$ in $(2)$, we get, $$1.18M +1.18F =1.1M +1.2F$$ $$\Rightarrow 0.08M =0.02F$$ $$\Rightarrow F=4M$$ Now from $(2)$ and $(3)$, we get, $$1.1M +1.2F =xM +1.1F$$ $$\Rightarrow (1.1-x)M =-0.1F =-0.4M$$ Thus, $$x=1.1+0.4=1.5$$ resulting in a $50$% rise to get the same rise in economy. Hope it helps.