A bicycle is available for ₹ 1,664 including tax. If the list price of the bicycle is ₹ 1,600, find

(i) the rate of Tax.

(ii) the price a customer will pay for the bicycle if the tax is increased by 6%.

(i) Given:

Sale price of bicycle = ₹ 1,664

List price of bicycle = ₹ 1,600

Let rate of tax = $x\%$

Tax on the sale = $x\%$ of ₹ 1,600

$\Rightarrow\dfrac{x}{100} \times ₹ 1,600\\[1em] \Rightarrow\dfrac{1,600x}{100}\\[1em] \Rightarrow 16x\\[1em]$

The amount to be paid = Sale price of bicycle

$\Rightarrow 1,600 + \text{x\% of 1,600} = 1,664\\[1em] \Rightarrow 1,600 + 16x = 1,664\\[1em] \Rightarrow 16x = 1,664 - 1,600\\[1em] \Rightarrow 16x = 64\\[1em] \Rightarrow x = \dfrac{64}{16}\\[1em] \Rightarrow x = 4\%\\[1em]$

Hence the rate of Tax = $4\%$

(ii) Given:

List price of bicycle = ₹ 1,600

Tax is increased by 6%, means (4% + 6%) = 10% of marked price.

Increased Tax = 10% of ₹ 1,600

$\Rightarrow\dfrac{10}{100} \times 1,600\\[1em] \Rightarrow\dfrac{16,000}{100}\\[1em] \Rightarrow 160$

Total amount to be paid = ₹ 1,600 + ₹ 160

= ₹ 1,760

Hence, the price a customer will pay for the bicycle = ₹ 1,760.