Question

The marked price of two articles together is Rs.6.000. The sales tax on article A is 8% and that on article B is 10%. If on selling both the articles, the total sales tax collected is Rs.552, find the sum of the marked price of each of the articles and B.

Answer 1

Hint: Assume a marked price of A and according to solve the question by finding the percentage of sales tax collected. It is given in the question that the total sales tax is 552.
To find the percentage the formula is: ${\displaystyle \frac{\text{given}\text{amount}}{\text{total}\text{amount}}}\times 100$
And to find the amount from a given percentage the formula is: ${\displaystyle \frac{\text{amount}\text{in}\text{percentage}(a{}^0/{}_0)\times \text{total}\text{amount}\text{of}\text{that}\text{percentage}}{100}}$

Complete step by step solution: Given that,
The total marked price of 2 articles together is 6000,
Sales tax on A is 8%
Sales tax on B is 10%
The total sales tax on selling both the articles = 552
then, we have to calculate the marked price of each article.
Therefore, we will assume the marked price as some variable.
Let the marked price of A= Rs x.
and the marked price of B = Rs. (6000 − x)
Sales tax on A = 8% of x
= Rs $({\displaystyle \frac{{\displaystyle \frac{2}{8}}}{{\displaystyle \frac{100}{25}}}}\times x)={\displaystyle \frac{2x}{25}}$
Sales tax on B = 10% of (6000- x )
$={\displaystyle \frac{6000-x}{100}}\times 10$
          = Rs $\left({\displaystyle \frac{6000-x}{10}}\right)$
Now
According to the question
${\displaystyle \frac{2x}{5}}+{\displaystyle \frac{6000-x}{10}}=552$ ①
[The Sum of the sales tax = 552 (given)]
Solving $eq$ ⑩
$\Rightarrow {\displaystyle \frac{8x+60000-10x}{100}}=552$
$=60000-2x=55200$
$\Rightarrow 2x=4800$
$\Rightarrow x=2400$
Therefore the marked price of A = Rs 2400
and the marked price of B = Rs (6000-x)
               = Rs (6000-2400 )
               = Rs 3600

Note: In this type of question do not assume 2 variables. With one variable we can solve this question. Here we were dealing with tax which is paid annually. It’s important to understand the rate of interest. If we are dealing with interest then it can be monthly also. So, while solving such a question please keep our eyes on this.