Question

4/15 of 5/7 of a number is greater than 4/9 of 2/5 of the same number by 8 . What is half of thenumber ?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{number}\mathrm{be}\mathrm{x}. \\ \mathrm{Then},\frac{4}{15}\mathrm{of}\frac{5}{7}\mathrm{of}\mathrm{the}\mathrm{number}=\frac{4}{15}\times \frac{5}{7}\times \mathrm{x}=\frac{4}{21}\mathrm{x} \\ \mathrm{Also},\frac{4}{9}\mathrm{of}\frac{2}{5}\mathrm{of}\mathrm{the}\mathrm{number}=\frac{4}{9}\times \frac{2}{5}\times \mathrm{x}=\frac{8}{45}\mathrm{x} \\ \mathrm{According}\mathrm{to}\mathrm{the}\mathrm{question},\mathrm{we}\mathrm{have} \\ \frac{4}{21}\mathrm{x}=\frac{8}{45}\mathrm{x}+8 \\ \Rightarrow \frac{4}{21}\mathrm{x}-\frac{8}{45}\mathrm{x}=8\left[\mathrm{Subtracting}\frac{8}{45}\mathrm{x}\mathrm{from}\mathrm{both}\mathrm{sides}\right] \\ \Rightarrow \frac{4\times 15}{315}\mathrm{x}-\frac{8\times 7}{315}\mathrm{x}=8\left[\mathrm{L}.\mathrm{C}.\mathrm{M}.\mathrm{of}21\mathrm{and}45\mathrm{is}315\right] \\ \Rightarrow \frac{4}{315}\mathrm{x}=8 \\ \Rightarrow \mathrm{x}=8\times \frac{315}{4}=630.\left[\mathrm{Multiplying}\mathrm{both}\mathrm{sides}\mathrm{by}\frac{315}{4}\right] \\ \mathrm{The}\mathrm{required}\mathrm{number}\mathrm{is}630. \end{gathered}$$