When the rate of Tax is decreased from 9% to 6% for a coloured T.V.; Mrs Geeta will save ₹ 780 in buying this T.V. Find the list price of the T.V.

Let the list price of the T.V. be ₹ $x$.

Original Tax % = 9%

∴ Original Tax = 9% of ₹ $x$

= $\dfrac{9}{100} \times ₹ x$

= $\dfrac{9x}{100}$

Selling price of the T.V. = ₹ x + ₹ $\dfrac{9x}{100}$

= ₹ $\dfrac{100x}{100} + ₹ \dfrac{9x}{100}$

= ₹ $\dfrac{(100x + 9x)}{100}$

= ₹ $\dfrac{109x}{100}$

Reduced Tax % = 6%

∴ Reduced Tax = 6% of ₹ $x$

= $\dfrac{6}{100} \times ₹ x$

= $\dfrac{6x}{100}$

New Selling price of the T.V. = $₹ x + ₹ \dfrac{6x}{100}$

= ₹ $\dfrac{100x}{100} + ₹ \dfrac{6x}{100}$

= ₹ $\dfrac{(100x + 6x)}{100}$

= ₹ $\dfrac{106x}{100}$

Given, difference in the selling price = ₹ 780 [∵ Mrs Geeta saves ₹ 780]

Original S.P. - New S.P. = 780

$\Rightarrow \dfrac{109x}{100} - \dfrac{106x}{100} = 780\\[1em] \Rightarrow \dfrac{(109x - 106x)}{100} = 780\\[1em] \Rightarrow \dfrac{3x}{100} = 780\\[1em] \Rightarrow x = \dfrac{780 \times 100}{3}\\[1em] \Rightarrow x = \dfrac{78,000}{3}\\[1em] \Rightarrow x = 26,000$

Hence, the list price of the T.V. = ₹ 26,000.