The price of a T.V. set inclusive of tax of 9% is ₹ 13,407. Find its marked price. If tax is increased to 13%, how much more does the customer has to pay for the T.V. set ?

Given:

The selling price of a T.V. = ₹ 13,407

and, Tax = 9% of marked price

Let the marked price be ₹ $x$.

$x + \text{9\% of x} = ₹ 13,407\\[1em] \Rightarrow x + \dfrac{9}{100} \times x = ₹ 13,407\\[1em] \Rightarrow \dfrac{100x}{100} + \dfrac{9x}{100} = ₹ 13,407\\[1em] \Rightarrow \dfrac{(100x + 9x)}{100} = ₹ 13,407\\[1em] \Rightarrow \dfrac{109x}{100} = ₹ 13,407\\[1em] \Rightarrow x = ₹ \dfrac{13,407 \times 100}{109}\\[1em] \Rightarrow x = ₹ \dfrac{13,40,700}{109}\\[1em] \Rightarrow x = ₹ 12,300\\[1em]$

Marked price of the T.V. = ₹ 12,300

Increased Tax = 13% of marked price

$\Rightarrow\dfrac{13}{100} \times ₹ 12,300 \\[1em] \Rightarrow₹ \dfrac{1,59,900}{100} \\[1em] \Rightarrow ₹ 1,599$

Total amount paid = ₹ 12,300 + ₹ 1,599

= ₹ 13,899

Difference of selling price = ₹ 13,899 - ₹ 13,407

= ₹ 492

Hence, the cost of the T.V. is ₹ 12,300 and the customer has to pay ₹ 492 more for the T.V. when tax is increased by 13%.