Question

Gauri went to the stationers and bought things worth Rs.25 out of which 30 paise went on sales tax on taxable purchases. If the tax rate was $$6\mathrm{\%}$$, then what was the cost of the tax free items?
A. $$\mathrm{R}\mathrm{s}.15$$
B. $$\mathrm{R}\mathrm{s}.15.70$$
C. $$\mathrm{R}\mathrm{s}.19.70$$
D. $$\mathrm{R}\mathrm{s}.20$$

Answer 1

Hint: Here, we will find the amount of tax on taxable purchases by using the formula of rate of tax. We will then find the total amount paid on cost by adding sales tax and amount of tax on taxable purchases. We will find the cost of the tax-free items by subtracting the amount paid on tax from the total cost. Tax is an amount paid to the government for the items purchased.

Formula Used:
Rate of tax is given by the formula Rate of tax $$={\displaystyle \frac{x}{n}}\times 100$$ where $$x$$ is the sales tax on taxable purchases, $$n$$ is the amount of tax on taxable purchases

Complete step-by-step answer:
Let $$y$$ be the amount of tax on taxable purchases.
We know that the rate of tax is $$6\mathrm{\%}$$.
Here the sales tax is given in paise, so we will convert it into rupees by dividing it with 100.
We know $$\mathrm{R}\mathrm{s}.1=100\mathrm{p}\mathrm{a}\mathrm{i}\mathrm{s}\mathrm{e}$$, so
 $$30\mathrm{p}\mathrm{a}\mathrm{i}\mathrm{s}\mathrm{a}=\mathrm{R}\mathrm{s}.{\displaystyle \frac{30}{100}}=\mathrm{R}\mathrm{s}.0.30$$
Now by using the formula Rate of tax $$={\displaystyle \frac{x}{n}}\times 100$$, we get
 $$\Rightarrow 6={\displaystyle \frac{0.30}{y}}\times 100$$
On cross multiplication, we get
 $$\Rightarrow {\displaystyle \frac{6}{100}}\times y=0.30$$
Now, we will convert the decimal into fraction. Therefore, we get
 $$\Rightarrow {\displaystyle \frac{6}{100}}\times y={\displaystyle \frac{30}{100}}$$
By simplifying the equation, we get
 $$\Rightarrow 6y=30$$
Dividing both sides by 6, we get
 $$\Rightarrow y={\displaystyle \frac{30}{6}}$$
 $$\Rightarrow y=5$$
Thus, the amount of tax on taxable purchases is Rs. 5.
The total amount paid on tax is calculated by adding the amount of tax on taxable purchases and the sales tax on taxable purchases
Total amount paid on tax $$=$$ sales tax on taxable purchases $$+$$ Amount of tax on taxable purchases
Substituting the values in the above equation, we get
 $$\Rightarrow$$ Total amount paid on tax $$=\mathrm{R}\mathrm{s}.5+\mathrm{R}\mathrm{s}.0.30$$
 $$\Rightarrow$$ Total amount paid on tax $$=\mathrm{R}\mathrm{s}.5.30$$
Thus the cost of the tax free items is calculated by subtracting the total amount paid on tax from the total cost of the items.
Cost of the tax free items $$=\mathrm{R}\mathrm{s}.25-\mathrm{R}\mathrm{s}.5.30$$
 $$\Rightarrow$$ Cost of the tax free items $$=\mathrm{R}\mathrm{s}.19.70$$
Therefore, the cost of the tax free items is $$\mathrm{R}\mathrm{s}.19.70$$

Note: We should notice that the given sales tax on taxable purchases is the amount of tax paid for the total amount of tax of taxable purchases. The rate of tax formula is similar to the percentage formula. The tax amount should be paid only once for a particular product. We have to be clear that the amount of tax on taxable purchases and the sales tax on taxable purchases should be added and it should not be multiplied.