Question

By what per cent is Rs 2,000 less than Rs 2,400? Is it the same as the per cent by which Rs 2,400 is
more than Rs2,000?
10) A music system was sold for Rs 5760 after giving successive discounts of 10% and 20 %
respectively. What was the marked price?
11) What single discount is equivalent to two successive discounts of 30% and 10%?
12) A shopkeeper allows 15% discount and still

Answer 1

$$\begin{gathered} \left(2\right). \\ \mathrm{Let}\mathrm{the}\mathrm{MP}\mathrm{of}\mathrm{the}\mathrm{music}\mathrm{system}=\mathrm{Rs}\mathrm{x} \\ \mathrm{Rate}\mathrm{of}\mathrm{first}\mathrm{discount}=20\% \\ \mathrm{First}\mathrm{discount}=20\%\mathrm{of}\mathrm{Rs}\mathrm{x}=\mathrm{Rs}\left(\frac{\mathrm{x}}{5}\right) \\ \mathrm{Now},\mathrm{price}\mathrm{after}\mathrm{first}\mathrm{discount}=\mathrm{x}-\frac{\mathrm{x}}{5}=\mathrm{Rs}\left(\frac{4\mathrm{x}}{5}\right) \\ \mathrm{Rate}\mathrm{of}\mathrm{second}\mathrm{discount}=10\% \\ \mathrm{second}\mathrm{discount}=10\%\mathrm{of}\frac{4\mathrm{x}}{5}=\mathrm{Rs}\left[\frac{2\mathrm{x}}{25}\right] \\ \mathrm{Price}\mathrm{after}\mathrm{second}\mathrm{discount}=\frac{4\mathrm{x}}{5}-\frac{2\mathrm{x}}{25}=\mathrm{Rs}\left(\frac{18\mathrm{x}}{25}\right) \\ \mathrm{Now},\mathrm{according}\mathrm{to}\mathrm{question}, \\ \frac{18\mathrm{x}}{25}=5760 \\ \Rightarrow \mathrm{x}=8000 \\ \mathrm{So},\mathrm{MP}\mathrm{of}\mathrm{music}\mathrm{system}=\mathrm{Rs}8000 \end{gathered}$$