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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?

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19.86%.

73.75%.

13.75%.

17.35%.

answer is A.

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Detailed Solution

Given selling price for cosmetic item including VAT=Rs.345 .
Rate of value added tax for cosmetic item = 15% .
Selling price for purse including VAT=Rs.110 .
Rate of value added tax for purse = 10%.

Cost price = Selling price − Cost price × Rate of value added tax 100

Let the cost price of the cosmetic item be Rs.X and the cost price of the purse be Rs. Y For cosmetic item:

Cost price × Rate of value added tax 100 = Rs . X × 15 100 ⇒ Rs .15 X 100 ⇒ Rs .0 .15 X

For purse,

Cost price × Rate of value added tax 100 = Rs . Y × 10 100 ⇒ Rs .10 X 100 ⇒ Rs .0 .1 X

For cosmetic item,

Selling price = Cost price + Cost price × Rate of value added tax 100 ⇒ Rs .345 = X + 0.15 X ⇒ Rs .345 = 1.15 X ⇒ X = Rs . 345 1.15 ⇒ X = Rs .300

The cost price of the cosmetic item is Rs.300.
For purse,

Selling price = Cost price + Cost price × Rate of value added tax 100 ⇒ Rs .110 = X + 0.1 X ⇒ Rs .110 = 1.1 X ⇒ X = Rs . 110 1.1 ⇒ X = Rs .100

The cost price of the puese is Rs.100.
The total cost price for cosmetic item and purse is =Rs.300+Rs.100

⇒

Rs.400.
The total selling price for cosmetic item and purse is =Rs.345+Rs.110

⇒

Rs.455.
Let the rate of value added tax on the whole transaction be r%.

Cost price × Rate of value added tax 100 = Rs .400 × r 100 Total cost price = Rs .400 ⇒ Rs .400 r 100 ⇒ Rs .4 r

Now,

Cost price = Selling price − Cost price × Rate of value added tax 100 ⇒ Rs .400 = Rs .455 − Rs .4 r [Total selling price = Rs .455] ⇒ Rs .4 r = Rs .455 − Rs .400 ⇒ r = 554 ⇒ r = 13.75 %

Hence, the rate of value-added tax charged on the whole transaction is 13.75%.
Therefore, option (1) is correct.

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