Question

2000 tickets were sold in an exhibition on Saturday. The cost of ticket for adult Is 4 rupees and for child is 2 Rupees. The total amount collected on Saturday was 6400 Rupees. Find the number of adult and child ticket sold on Saturday?

Answer 1

$$\begin{gathered} \mathrm{Dear}\mathrm{Student}, \\ \mathrm{Let}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{adult}\mathrm{tickets}\mathrm{sold}=\mathrm{x} \\ \mathrm{Let}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{child}\mathrm{tickets}\mathrm{sold}=\mathrm{y} \\ \mathrm{Now},\mathrm{x}+\mathrm{y}=2000.....\left(1\right) \\ \mathrm{Now},\mathrm{cost}\mathrm{of}1\mathrm{adult}\mathrm{ticket}=\mathrm{Rs}4 \\ \mathrm{Cost}\mathrm{of}\mathrm{x}\mathrm{adult}\mathrm{tickets}=\mathrm{Rs}4\mathrm{x} \\ \mathrm{Cost}\mathrm{of}1\mathrm{child}\mathrm{ticket}=\mathrm{Rs}2 \\ \mathrm{Cost}\mathrm{of}\mathrm{y}\mathrm{child}\mathrm{tickets}=\mathrm{Rs}2\mathrm{y} \\ \mathrm{Now},4\mathrm{x}+2\mathrm{y}=6400 \\ \Rightarrow 2\mathrm{x}+\mathrm{y}=3200.....\left(2\right) \\ \mathrm{Subtracting}\left(1\right)\mathrm{from}\left(2\right),\mathrm{we}\mathrm{get} \\ \mathrm{x}=1200 \\ \mathrm{Put}\mathrm{x}=1200\mathrm{in}\left(1\right),\mathrm{we}\mathrm{get} \\ 1200+\mathrm{y}=2000 \\ \Rightarrow \mathrm{y}=800 \\ \mathrm{So},\mathrm{number}\mathrm{of}\mathrm{adult}\mathrm{tickets}\mathrm{sold}=1200 \\ \mathrm{number}\mathrm{of}\mathrm{child}\mathrm{tickets}\mathrm{sold}=800 \\ \mathrm{Regards} \end{gathered}$$