The price of an article is ₹ 8,250 which includes tax at 10%. Find how much more or less does a customer pay for the article, if the tax on the article:

(i) increases to 15%

(ii) decreases to 6%

(iii) increases by 2%

(iv) decreases by 3%.

Given:

The selling price of an article = ₹ 8,250

and, Tax = 10% of marked price

Let the marked price be ₹ $x$.

$x + \text{10\% of x} = ₹ 8,250\\[1em] \Rightarrow x + \dfrac{10}{100} \times x = ₹ 8,250\\[1em] \Rightarrow x + \dfrac{1}{10} \times x = ₹ 8,250\\[1em] \Rightarrow \dfrac{10x}{10} + \dfrac{x}{10} = ₹ 8,250\\[1em] \Rightarrow \dfrac{(10x + x)}{10} = ₹ 8,250\\[1em] \Rightarrow \dfrac{11x}{10} = ₹ 8,250\\[1em] \Rightarrow x = ₹ \dfrac{8,250 \times 10}{11}\\[1em] \Rightarrow x = ₹ \dfrac{82,500}{11}\\[1em] \Rightarrow x = ₹ 7,500\\[1em]$

(i) Marked price of the article = ₹ 7,500

And, Tax = 15% of marked price

$\Rightarrow\dfrac{15}{100} \times ₹ 7,500 \\[1em] \Rightarrow₹ \dfrac{1,12,500}{100} \\[1em] \Rightarrow ₹ 1,125$

Total amount paid = ₹ 7,500 + ₹ 1,125

= ₹ 8,625

Difference in selling price = ₹ 8,625 - ₹ 8,250

= ₹ 375

Hence, the customer has to pay ₹ 375 more for the article when tax is increased by 15%.

(ii) Marked price of the article = ₹ 7,500

And, Tax = 6% of marked price

$\Rightarrow\dfrac{6}{100} \times ₹ 7,500 \\[1em] \Rightarrow₹ \dfrac{45,000}{100} \\[1em] \Rightarrow ₹ 450$

Total amount paid = ₹ 7,500 + ₹ 450

= ₹ 7,950

Difference in selling price = ₹ 8,250 - ₹ 7,950

= ₹ 300

Hence, the customer has to pay ₹ 300 less for the article when tax was decreased by 6%.

(iii) Marked price of the article = ₹ 7,500

Tax is increased by 2% means (10% + 2%) = 12%

Increased Tax = 12% of marked price

$\Rightarrow\dfrac{12}{100} \times ₹ 7,500 \\[1em] \Rightarrow₹ \dfrac{90,000}{100} \\[1em] \Rightarrow ₹ 900$

Total amount paid = ₹ 7,500 + ₹ 900

= ₹ 8,400

Difference in selling price = ₹ 8,400 - ₹ 8,250

= ₹ 150

Hence, the customer has to pay ₹ 150 more for the article when tax is increased to 2%.

(iv) Marked price of the article = ₹ 7,500

Tax is decreased by 3% means (10% - 3%) = 7%.

Decreased Tax = 7% of marked price

$\Rightarrow\dfrac{7}{100} \times ₹ 7,500 \\[1em] \Rightarrow₹ \dfrac{52,500}{100} \\[1em] \Rightarrow ₹ 525$

Total amount paid = ₹ 7,500 + ₹ 525

= ₹ 8,025

Difference in selling price = ₹ 8,250 - ₹ 8,025

= ₹ 225

Hence, the customer has to pay ₹ 225 less for the article when tax is decreased to 3%.