Due to a reduction of 6.25% in the price of sugar a man is able to buy 1kg more for Rs 120. Find the reduction rate of sugar
Answers
Answer:
Rs 1/30 per kilogram
Step-by-step explanation:
Let the initial amount of sugar be x kg.
With 120 initially one is able to purchase x kg.
However when the price is reduced by 6.25% the amount that can be purchased is (x + 1) kg.
The initial cost of sugar per kilograms is :
120/x
When this is reduced by 6.25% we get :
(100% - 6.25%) of 120/ x :
= 93.75/100 × 120/x = 112.5/x......1)
The new price per kilogram can also be represented as :
120/(x + 1)..............2)
We equate 1 and 2 since they represent the same quantity :
120/(x + 1) = 112.5/x
120x = 112.5(x + 1)
120x = 112.5x + 112.5
120x - 112.5x = 112.5
7.5x = 112.5
x = 112.5/7.5 = 15
The initial amount is 15 kilograms.
The initial price of sugar = 120/15 = 8
The price after reduction = 120/16 = 7.5
The price reduces by Rs 0.5.
0.5/15 = 1/30
The reduction rate is Rs 1/30 per kilogram.