When the price of sugar decrease by 10%, a man could buy 1 kg more for Rs. 270. Then, the original price of sugar per kg is

When the price of sugar decrease by 10%, a man could buy 1 kg more for Rs. 270. Then, the original price of sugar per kg is
1). Rs. 25
2). Rs. 30
3). Rs. 27
4). Rs. 32

Let the original price of the sugar per kg be Rs. X. Let the quantity of sugar purchased initially be Y units in Rs. 270.

Thus, X × Y = 270 ….(1)

Given: Price of sugar decreased by 10%.

∴New price of sugar per Kg $( = \;X - \frac{{10}}{{100}}X)$

= 0.9X

Since the man could buy 1 more kg on his reduction of price, hence

⇒ Quantity of sugar purchased = Y + 1

As the total expenditure remains the same i.e. Rs. 270, therefore

⇒ 0.9X × (Y + 1) = 270 …(2)

Dividing equation (1) by (2), we get

$( \Rightarrow \frac{Y}{{0.9 \times \left( {Y + 1} \right)}} = 1)$

⇒ Y = 0.9Y + 0.9

⇒ Y = 9 units

∴ From equation (1) we get, X = Rs. 30

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