Question

Reduction of 30% in the price of tea enables a person to buy 3 kg more for ₹20 . Find the original price per kg of tea

Answer 1

Answer:

The original price of tea before reduction was approximately ₹ 2.86/kg

Step-by-step explanation:

Let the original price of tea be ₹ x/kg.

We are given that the price was reduced by 30%.

That implies, the new price of tea would be ₹ $x - \frac{30}{100} * x$

= ₹ $\frac{100x - 30x}{100} = \frac{70x}{100} = \frac{7x}{10}$.

Since the original price per kg was ₹ x,

∴ for ₹20, $\frac{20}{x}$ kg of tea could be bought.

According to the question, due to the reduction in price, for ₹20, 3kg more tea can be bought now.

Amount of tea that can be bought for ₹20 in the reduced price of $\frac{7x}{10}$ is $\frac{20}{\frac{7x}{10} } = \frac{200}{7x} kg$

Thus, we have,

$\frac{20}{x} + 3 = \frac{200}{7x}$

⇒ $\frac{20 + 3x}{x} = \frac{200}{7x}$

⇒ $\frac{20 + 3x}{1} = \frac{200}{7}$

⇒ $7 (20 + 3x) = 200$

⇒ $140 + 21x = 200$

⇒ $21x = 60$

⇒ $x = \frac{60}{21}$ ≅ $2.86$

Thus, the original price of tea before reduction was ₹ 2.86/kg