Question

A reduction of rs 2 per kg enables a man to purchase 2kg more tea for rs 8. Find the original price of tea kg

Answer 1

The original price of tea is Rs. 4 per kg.

• Let the original price of tea be Rs. x per kg.

• Reduction in price per kg = Rs. 2

Quantity of tea that can be bought for Rs. 8 at this price rate = 8 / x

• Reduced price of tea per kg = Rs. (x - 2)

Quantity of tea that can be bought for Rs. 8 at the reduced rate = 8 / (x -2)

• According to the question,

{8 / (x -2)} - (8 / x) = 2

=> { 8x - 8 (x - 2) } / x (x -2) = 2

=> 8x - 8x + 16 = 2x (x -2)

=> 16 = 2x² - 4x

=> 2x² - 4x - 16 = 0

=> 2x² - 8x + 4x - 16 = 0

=> 2x (x - 4) + 4 (x - 4) = 0

=> (x - 4) (2x + 4) = 0

=> x - 4 = 0,   2x + 4 = 0

=> x = 4, 2x = -4

=> x = 4,  x = -4 / 2 = -2

• Since price cannot be negative, -2 is discarded.

Therefore, the original price of tea was Rs. 4 per kg.