a reduction of 20% in the price of sugar enables a purchaser to obtain 2.5 kg more for Rs.160.find the original rate and the reduced price per kg.

find the original rate ?

you meant: find the original price ?

let original price be x
.8x = 160
x = 160/.8 = 200

but that is for 2.5 kg
so original price per kg = 200/2.5 = 80
reduced price per kg = 160/2.5 = 64

notice that 64 equals 80% of 80

To solve this problem, we need to set up an equation based on the given information.

Let's denote the original price per kilogram of sugar as "x."

According to the problem, a 20% reduction in price enables the purchaser to obtain 2.5 kg more for Rs.160.

So, the reduced price per kilogram of sugar would be (x - 20% of x) = (x - 0.2x) = 0.8x.

The equation can be set up as follows:

2.5 kg * (x - 0.8x) = Rs. 160

Simplifying the equation, we have:

2.5 * 0.2x = 160

0.5x = 160

x = 160 / 0.5

x = Rs. 320

The original rate of sugar per kilogram is Rs. 320.

To find the reduced price per kilogram, we substitute the original price into the equation for the reduced price:

Reduced price = 0.8 * Rs. 320 = Rs. 256

Therefore, the reduced price per kilogram of sugar is Rs. 256.