Answer :
The original price per kilo of sugar was determined by equating the difference between the quantities bought before and after a 20% price reduction to 2.5 kilos. The computation involved solving a linear equation to find the original price, which turns out to be $32 per kilo.
You asked about determining the original price per kilo of sugar given that a 20% reduction allows a purchaser to obtain an additional 2 1/2 kilos for $160. To solve this problem, we first need to understand the effect of the price reduction on the quantity that can be bought with a fixed sum of money.
Let x be the original price per kilo. With the reduction, the new price per kilo is 0.8x. For $160, before the price reduction, the purchaser could buy $160/x kilos. After the price reduction, the purchaser can buy $160/(0.8x) kilos. The difference in the quantity bought is given by:
$160/(0.8x) - $160/x = 2.5 kilos
To find the value of x, solve the equation:
(200)/(8x) - (160)/(x) = 2.5
Multiplying through by 8x to eliminate fractions gives:200 - 1280 = 20x
Solving for x gives x = 32. Therefore, the original price per kilo of sugar was $32.
So the correct answer is:d) $32 per kilo
