Name: Calculation of Taxes for Purchased Goods
Uploaded: 2019-07-19
Duration: 7 min 2 s
Description: A small amount for all the purchased goods is paid to the government. It is called sales tax. In this video, learn about the types of taxes and how taxes are...

Question

A reduction of

10 %

in the price of wheat would enable a man to buy

2 kg

more in

₹ 30

. Find the reduced price and original price of wheat.

Accepted Answer

Let the original price of the sugar be $₹ x$ per $kg$ .

So, the quantity of sugar that can be bought at $₹ 30$ is $\frac{30}{x} kg$ .

Given that the price of sugar is reduced by $10 %$ .

So, the reduced price of the sugar per $kg$ is $₹ x \times (1 - \frac{10}{100}) = ₹ \frac{9}{10} x$ .

So, the quantity of sugar that can be bought at $₹ 30$ at the reduced price is $\frac{30}{\frac{9 x}{10}} = \frac{300}{9 x} = \frac{100}{3 x} kg$ .

By the given condition of the problem, we get, $\frac{100}{3 x} - \frac{30}{x} = 2$

$\Rightarrow \frac{1}{x} [\frac{100}{3} - \frac{30}{1}] = 2$

$\Rightarrow \frac{1}{x} [\frac{100 - 90}{3}] = 2$

$\Rightarrow \frac{1}{x} [\frac{10}{3}] = 2$

$\Rightarrow \frac{1}{x} = 2 \times \frac{3}{10} = \frac{3}{5}$

$\Rightarrow x = \frac{5}{3}$

Now, $\frac{9}{10} x = \frac{9}{10} \times \frac{5}{3} = \frac{3}{2}$ .

Therefore, the original price of the sugar per $kg$ is $₹ \frac{5}{3}$ and the reduced price of sugar per $kg$ is $₹ \frac{3}{2}$ .

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