Question

The price of a T.V set inclusive of Sales Tax of \[9\% \] is \[{\text{Rs}}.13,407\] . Find its marked price. If Sales Tax is increased to \[13\% \] , how much more does the customer have to pay for the T.V?
A. \[{\text{Rs}}.18,300;\,{\text{Rs}}.900\]
B. \[{\text{Rs}}.16,300;\,{\text{Rs}}.720\]
C. \[{\text{Rs}}.14,300;\,{\text{Rs}}.630\]
D. \[{\text{Rs}}.12,300;\,{\text{Rs}}.492\]

Answer 1

Hint: The question has two parts, in the first part we are asked to find out the marked price of the T.V set. Using the value of selling price and the Sales Tax given, find out the marked price of the T.V set. In the second part we asked if the Sales Tax is \[13\% \] then how much more amount the customer has to pay than he paid when the Sales Tax was \[9\% \] . For solving the second part use the marked price calculated in the first part to find out its selling price.

Complete step-by-step answer:
Given, when Sales Tax is \[T = 9\% \] the selling price of the T.V is \[S.P = {\text{Rs}}.13,407\] .
In the first part we are asked to calculate its marked price.
Let the marked price be \[x\] .
It is said that the selling price is inclusive of Sales Tax that is, Sales Tax is added to the marked price. The Sales Tax is \[9\% \] so, the added tax to the marked price will be \[9\% \] of the marked price that is,
 \[{\text{Tax}}\,{\text{added}} = 9\% \,{\text{of Marked price}}\]
 \[ \Rightarrow {\text{Tax}}\,{\text{added}} = 9\% \,{\text{of }}x\] (i)
The selling price of the T.V set will be the marked price plus the tax added so, we can write,
 \[S.P = {\text{Marked}}\,{\text{price}} + {\text{Tax}}\,{\text{added}}\]
Putting the value of marked price as \[x\] and tax added from equation (i) we get,
 \[S.P = x + 9\% \,{\text{of }}x\]
Putting the value of selling price, \[S.P = {\text{Rs}}.13,407\] we get,
 \[13407 = x + 9\% \,{\text{of }}x\]
 \[ \Rightarrow x + \dfrac{{9x}}{{100}} = 13407\]
 \[ \Rightarrow \dfrac{{100x + 9x}}{{100}} = 13407\]
 \[ \Rightarrow 109x = 13407 \times 100\]
 \[ \Rightarrow x = \dfrac{{13407 \times 100}}{{109}}\]
 \[ \Rightarrow x = {\text{Rs}}.12,300\]
Therefore, the marked price is \[{\text{Rs}}.12,300\]
In the second part, it is given that the Sales tax is increased to \[13\% \] and we have to find out how much more the customer has to pay for the T.V set.
Now, we have the value of marked price as, \[M.P = {\text{Rs}}.12,300\]
The tax added to the marked price when Sales tax is \[13\% \] is,
 \[{\text{Tax}}\,{\text{added}} = 13\% \,{\text{of }}M.P\]
Putting the value of \[M.P\] we get,
 \[{\text{Tax}}\,{\text{added}} = 13\% \,{\text{of Rs}}.12,300\]
 \[ \Rightarrow {\text{Tax}}\,{\text{added}} = \dfrac{{13}}{{100}}\, \times 12300\]
 \[ \Rightarrow {\text{Tax}}\,{\text{added}} = {\text{Rs}}.1599\]
Now, the selling price will be
 \[S.P = M.P + {\text{Tax}}\,{\text{added}}\]
Putting the value of \[M.P\] and tax added we get,
 \[S.P = 12300 + 1599\]
 \[ \Rightarrow S.P = {\text{Rs}}.13,899\]
When the Sales tax is \[9\% \] , the selling price is \[{\text{Rs}}.13,407\] and when the Sales tax is \[13\% \] the selling price is \[{\text{Rs}}.13,899\] . Therefore, the amount the customer has to pay more will be,
 \[{\text{amount}}\,{\text{to}}\,{\text{be}}\,{\text{paid}}\,{\text{more}} = {\text{Rs}}.13,899 - {\text{Rs}}.13,407 = {\text{Rs}}.492\]
Hence, the correct answer is option (D) \[{\text{Rs}}.12,300;\,{\text{Rs}}.492\]
So, the correct answer is “Option D”.

Note: In this question it was given that Sales Tax was included to the marked price, so we added the tax to the marked price. But, if it is given that there is a discount on the marked price that would mean the selling price will reduce and we have to subtract the discount amount from the marked price. So, while solving such types of questions carefully check the information whether there is decrease in selling price or increase in selling price.