# Shruti bought a set of cosmetic items for Rs 345 including 15% value added tax and a purse for Rs 110 including 10% VAT.

**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?

**Solution:**

Let the price of the cosmetic items be Rs. $x$ and $t h e p$ rice of the purse be Rs. $y$.

$\mathrm{VAT}=15 \%$ of $x=\frac{15 x}{100}=R s \cdot \frac{3 x}{20}$

$\mathrm{VAT}=10 \%$ of $y=\frac{10 y}{100}=R s . \frac{y}{10}$

So, SP of cosmetic items $=x+\frac{3 x}{20}=R s . \frac{23 x}{20}$

$\mathrm{SP}$ of purse $=\left(y+\frac{y}{10}\right)=R s . \frac{11 y}{10}$

But the selling price of the cosmetic items and the purse is Rs. 345 and Rs. 110 respectively.

So, $\frac{23 x}{20}=345$

$x=R s .300$

and

$\frac{11 y}{10}=110$

$11 y=1100$

$y=R s .100$

Total price $=$ Rs. $(300+100)=$ Rs. 400

Now,

Let the VAT on the whole transaction be $\mathrm{r} \%$.

$r \%$ of $400=\frac{r}{100} \times 400=4 r$

Total transaction $=$ Rs. $345+110=$ Rs. 455

So,

$4 r+400=455$

$4 r=55$

$r=\frac{55}{4}$

$=13.75$

Thus, VAT charged on the whole transaction is $13.75 \%$.