Mamta bought a set of cosmetic items for ₹ 660 including 10 % sales tax and a purse for ₹ 106 including 6 % sales tax. What percent is the sales tax charged on the whole purchase?

Given :

Mamata bought a set of cosmetics for Rs.660 including 10% sales tax and a purse for Rs. 106 including 6% sales tax.

To do :

We have to find the sales tax charged on the whole purchase.

Solution :

Let the price of the cosmetics be Rs.x and the price of the purse be Rs. y.

Sales tax on cosmetics $=$ 10% of x

                                         $ = \frac{10}{100}x$

                                          $= 0.1x$

This implies,

Selling price of cosmetics $= x+0.1x = 1.1x$

$Rs. 660 = 1.1x$

$x=\frac{660}{1.1}$

$x=\frac{6600}{11}$

$x=Rs. 600$

The price of cosmetics is Rs. 600.

Sales tax on Purse $=$ 6% of y

                                  $= \frac{6}{100} y$

                                  $= 0.06 y$

Selling price of Purse $= y+0.06y=1.06y$

$Rs. 106 = 1.06y$

$y=\frac{106}{1.06}$

$y=\frac{10600}{106}$

$y=Rs. 100$

The price of the Purse is Rs. 100.

The price of the whole purchase $= Rs.(600+100) = Rs. 700$

Sales tax charged on the whole purchase $= Rs.(660+106) - Rs. 700 = Rs. (766-700) = Rs. 66$

Let the percentage of sales tax on the whole purchase be r.

$66= \frac{r}{100} \times 700$

$r = \frac{66 \times 100}{700}$

$r=\frac{66}{7}$%

$r=9 \frac{3}{7}$%.

The percent of the sales tax charged on the whole purchase is $\frac{66}{7}$%.

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Updated on: 10-Oct-2022

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