A bag contains n coins of which five of them are counterfeit with heads on both sides and the rest are fair coins. If one coin is selected from the bag and tossed, the probability of getting head is 5/8 then n = 

A bag contains n coins of which five of them are counterfeit with heads on both sides and the rest are fair coins

$\mathrm{Let} \mathrm{C}=\mathrm{counterfeit} \mathrm{coin} , \mathrm{F}= \mathrm{Fair} \mathrm{coin}$

$\mathrm{P}\left(\mathrm{C}\right)=\frac{5}{\mathrm{n}},\mathrm{P}\left(\mathrm{F}\right)=\frac{\mathrm{n}-5}{\mathrm{n}}$

$P\left(H/C\right)=1,P\left(H/F\right)=\frac{1}{2}$

$P\left(H\right)=\frac{5}{8}$

$P\left(H\right)=P\left(C\right)P\left(H/C\right)+P\left(F\right)P\left(H/F\right)$

$\frac{5}{8}=\frac{5}{n}\left(1\right)+\frac{n-5}{n}\left(\frac{1}{2}\right)$

$\frac{5}{8}=\frac{10+\mathrm{n}-5}{2\mathrm{n}}\Rightarrow 5\mathrm{n}=4\left(\mathrm{n}+5\right)\Rightarrow \mathrm{n}=20$