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?

Explanation

Let the price of the cosmetic items be `x` and the price of the purse be `y`.
VAT`=15%` of `x`
`=x×15/100`
​`=3x/20`
​VAT`=10%` of `y`
`=y×10/100`
​`= y/10`
​The selling price of cosmetic items `=x+3x/20`
`​ =23x/20`
S.P of the purse `=y+y/10`
`=11y/10`
But selling price of the cosmetic and purse `345` and Rs.`110`, respectively.
So,
`23x/20=345`
`x=345× 20/23`
`x=`Rs.`300`
So,`11y/10 =110`
`y=110×(10/11)`
`y=`Rs.`100`
Therefore,
Total price `=(300+100)=`Rs.`400`
Now,
Let the VAT on the whole transaction be `z%`
So,
`z×(400/100)​=4z`
Total transaction `=345+110=455`
Thus,
`4z+400=455`
`z= (455−400)/4 `
`z=13.75%`
Hence, VAT on the whole transaction is `13.75%`.