Jordan K. answered • 10/11/15
Tutor
4.9
(79)
Nationally Certified Math Teacher (grades 6 through 12)
Hi Amey,
Let's begin by determining the original price (x):
(25/4)% = 6.25% = 6.25/100 = 0.0625
reduced price = 120 rs
x - 0.0625x = 120
0.9375x = 120
x = 120/0.9375
x = 128 rs (original price)
Next, let's calculate at what sugar amounts
(x and x+1) will the reduced price yield one more kg of sugar than the original price (this is an inverse relationship - more sugar for less money):
128 : 120 = x+1 : x
128/120 = x+1:x
16/15 = x+1/x
x+1 = 16 kgs of sugar at reduced price
x = 15 kgs of sugar at original price
Now, we can calculate the original unit price (rate of sugar) and the reduced unit price (rate of sugar):
128 rs / 15 kgs = 8.53 rs / kg (orig. unit price)
120 rs / 16 kgs = 7.5 rs / kg (reduced unit price)
As we would expect to see - the reduced unit price is lower than the original unit price.
Thanks for submitting this problem and glad to help.
God bless, Jordan.
Amey B.
Report
10/11/15
Amey B.
a man is able to buy 1 kg more for Rs 120
how you know that this 120 is not 1 kg price
because this is very confusing sentence it has two conclusion
one conclusion is 1 kg is Rs 120
second conclusion is whatever whole kg is for Rs 120
how you come to know what is right please give me definite explanation
Report
10/11/15
Jordan K.
The information given in the problem dictated the approach to our solution. To clarify - will explain the steps taken to get our answer:
1. Calculate the original price relative to the given reduced price of 120 rs. using the given price reduction percentage.
2. Use the given relationship that at 120 rs. - 1 more kg could be purchased than at the original price - in order to find the # of kgs for which this relationship is true.
3. Divide each price (before and after the price reduction ) by the # of kgs calculated in step 2 to get the unit price (price per kg) before and after the price reduction.
Trust the above helps to make everything clear.
Report
10/11/15
Jordan K.
Hi Amey,
Need to amend my answer - had steps 2 and 3 reversed. Will let you know when done.
Sorry for the confusion.
Report
10/11/15
Jordan K.
Hi Amey,
Solution has been modified and all steps are now clearly explained.
Thanks for your patience.
Report
10/11/15
Amey B.
previous my question was i want to know that how you determine that 120 is price of 16 kg because in question
a man is able to buy 1 kg more for Rs 120 other way is he purchased 1 kg extra for 120
due to reduction of 25/4% in the price of sugar how you determine that 25/4% reduction is per kg
please sir i dont convert math language into english i want to know if you have any guidance then give me
Report
10/14/15
Jordan K.
Hi Amey,
Will try one more run at trying to explain my understanding of the problem and my reasoning for the solution.
My understanding of the problem is that at 120 rs he is able to buy an additional 1 kg of sugar than he would have been able to buy at the original price.
This is why I understood the 120 rs to be the reduced price and then was able to calculate the original price using the discount percentage.
Then knowing the reduced price (120 rs) and the calculated original price (128 rs) we were able to find the amount of sugar bought at both prices where the difference in the amounts is 1 kg - using this inverse proportion (higher price : lower price = more sugar : less sugar):
orig. price : red. price = x + 1 : x
128 : 120 = x + 1 : x
x + 1 = 1 kg more sugar at 120 rs
x = kg sugar at 128 rs
The ratio (128/120) reduced to lowest terms is 16/15, which gave us the 1 kg difference amount of sugar between the two prices:
16 kg (x + 1) bought for 120 rs
15 kg (x) bought for 128 rs
Trust this helps.
Regards, Jordan.
Report
10/14/15
Amey B.
10/11/15