Question

Shruti bought a set of cosmetic items for Rs 345 including 15% value added tax and a purse for Rs 110 including 10% VAT. What percent is the VAT charged on the whole transaction?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{price}\mathrm{of}the\mathrm{cosmetic}\mathrm{items}\mathrm{be}\mathrm{R}s.x\mathrm{and}thep\mathrm{rice}\mathrm{of}the\mathrm{purse}\mathrm{be}\mathrm{Rs}.y. \\ \mathrm{VAT}=15\%\mathrm{of}x=\frac{15x}{100}=Rs.\frac{3x}{20} \\ \mathrm{VAT}=10\%\mathrm{of}y=\frac{10y}{100}=Rs.\frac{y}{10} \\ \mathrm{So},\mathrm{SP}\mathrm{of}\mathrm{cosmetic}\mathrm{items}=x+\frac{3x}{20}=Rs.\frac{23x}{20} \\ \mathrm{SP}\mathrm{of}\mathrm{purse}=\left(y+\frac{y}{10}\right)=Rs.\frac{11y}{10} \\ \mathrm{But}the\mathrm{selling}\mathrm{price}\mathrm{of}the\mathrm{cosmetic}items\mathrm{and}the\mathrm{purse}is\mathrm{Rs}.345\mathrm{and}\mathrm{Rs}.110respectively. \\ \mathrm{So},\frac{23x}{20}=345 \\ x=Rs.300 \\ \mathrm{and} \\ \frac{11y}{10}=110 \\ 11y=1100 \\ y=Rs.100 \\ \mathrm{Total}\mathrm{price}=\mathrm{Rs}.(300+100)=\mathrm{Rs}.400 \\ Now, \\ Letthe\mathrm{VAT}\mathrm{on}\mathrm{the}\mathrm{whole}\mathrm{transaction}\mathrm{be}\mathrm{r}\%. \\ r\%\mathrm{of}400=\frac{r}{100}\times 400=4r \\ T\mathrm{otal}\mathrm{transaction}=Rs.345+110=Rs.455 \\ \mathrm{So}, \\ 4r+400=455 \\ 4r=55 \\ r=\frac{55}{4} \\ =13.75 \\ \mathrm{Thus},\mathrm{VAT}charged\mathrm{on}the\mathrm{whole}\mathrm{transaction}\mathrm{is}13.75\%. \end{gathered}$$