Question

A calculator manufacturer’s manufacturing cost of a calculator is rupees Rs. $900$ . GST is $18\%$ . He manufactured $120$ such calculators. He marked up each by $50\%$ and sold to a dealer at a discount of $10\%$ . Find the final price paid by the dealer. Also find the total GST received by the State Government​.

Answer 1

Hint: For questions like these we will first find the cost of one calculator including the GST so we will find $18\%$ of the cost price and then add it to the cost price and then we will increase the price by $50\%$. After that, we will subtract $10\%$ of the total marked up price and finally subtract it from the marked up price and then we will have the total selling price. We will multiply it by $120$to find the final price paid by the dealer. Now, to find the selling price without GST by dividing it by $1.18$, subtract the selling price excluding GST from the original selling price and this way we will get the GST paid for one calculator multiply it by $120$ to get the total GST and finally divide it by $2$ to get the total GST received by the State Government​.

Complete step by step answer:
So it is given in the question that the manufacturing cost of one calculator: Rs. $900$.
And it is given that the GST is $18\%$, therefore the GST = \[\dfrac{18}{100}\times 900=\text{ Rs}\text{. }162\]
Therefore, the manufacturing cost of one calculator including the GST is $900+162=\text{ Rs}\text{. 10}62$ .
It is given that the marked up $50\%$ , now we know that Marked Price = $CP+\left( \dfrac{\text{mark up }\!\!\%\!\!\text{ }}{100} \right)\times CP$
Therefore, the marked price of the calculator will be: \[1062+\left( \dfrac{50}{100}\times 1062 \right)=\text{Rs}\text{. }1593\]
And it is given that the calculator is sold at $10\%$ discount, this discount is given on marked price therefore the discount is $\left( \dfrac{10}{100} \right)\times 1593=159.3$ ,
Therefore, $\text{Selling Price}=\text{Marked Price}-\text{Discount}=1593.3-159.3=Rs.\text{ 1433}\text{.7}$ .
Now for the price paid by dealer for $120$ calculator is $1433.7\times 120=\text{Rs}\text{. 172044}$
Now, we will see that the selling price without the GST is: $\dfrac{1433.7}{1.18}=\text{Rs}\text{. }1215$ ,
So the total GST paid for one calculator:
Price with GST – Price without GST = $1433.7-1215=\text{Rs}\text{. }218.7$
So, now the total GST paid for $120$ calculator: $218.7\times 120=\text{Rs}\text{. }26244$ , therefore, the GST received by state government: $\dfrac{26244}{2}=\text{Rs}\text{. }13122$
So, the final price paid for calculators by the dealer is $\text{Rs}\text{. 172044}$ and the GST received by state government is $\text{Rs}\text{. }13122$.

Note:
 In these types of questions, the student may make the mistake with the calculations while finding the marked up price. Remember to multiply $120$ for the total selling price and the total GST. Discounts do not really mean that the owner will be in loss as sometimes there are marked-up prices.