Please send answer

Please send answer O There are few adults and children in a restaurant. If — of the people in the restaurant are adults and there are 90 more children than adults, then how many children are there in the restaurant? (A) 180 (B) 200 (C) 225 (D) 230

Dear Student,

$$\begin{gathered} \mathrm{Let} \mathrm{the} \mathrm{number} \mathrm{of} \mathrm{people} \mathrm{in} \mathrm{the} \mathrm{restaurant} \mathrm{be} \mathrm{x}. \\ \mathrm{Then}, \mathrm{number} \mathrm{of} \mathrm{adults} = \frac{3}{8}\mathrm{x} \\ \mathrm{Number} \mathrm{of} \mathrm{childrens} =\mathrm{x}-\frac{3\mathrm{x}}{8} = \frac{8\mathrm{x}-3\mathrm{x}}{8} = \frac{5\mathrm{x}}{8} \\ \mathrm{According} \mathrm{to} \mathrm{question}, \mathrm{number} \mathrm{of} \mathrm{childrens} = \frac{3\mathrm{x}}{8}+90 \\ \mathrm{So}, \frac{5\mathrm{x}}{8}=\frac{3\mathrm{x}}{8}+90 \\ \frac{5\mathrm{x}}{8} = \frac{3\mathrm{x}+90\times 8}{8} \\ 40\mathrm{x} =24\mathrm{x}+5760 \\ 16\mathrm{x} = 5760 \\ \mathrm{x} = \frac{5760}{16} \\ \mathrm{x} = 360 \\ \mathrm{So}, \mathrm{there} \mathrm{are} \mathrm{total} 360 \mathrm{people} \mathrm{in} \mathrm{the} \mathrm{restaurant} \\ \mathrm{Number} \mathrm{of} \mathrm{children} = \frac{3\times 360}{8}+90 \\ \mathrm{Number} \mathrm{of} \mathrm{children} = 135+90 \\ \mathrm{Number} \mathrm{of} \mathrm{children} = 225 \\ \mathrm{Hence}, \mathrm{option} \left(\mathrm{C}\right) \mathrm{is} \mathrm{correct} \end{gathered}$$

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