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Question

On selling a tea set at 5%loss and a lemon set at 15% gain,a shopkeeper gains ₹70. If he sells the tea set at 5%gain and the lemon set at 10% gain , he gains ₹130 . Find the cost price of lemon set and tea set.


Solution

Solution:-
Let the cost of tea set be Rs 'x' and the cost of lemon set be Rs 'y'.
The shopkeeper sells a tea set at 5 % loss and a lemon set ate 15 % gain.
So, the loss on tea set = x*5/100
And the gain on lemon set = y*15/100
Total gain = 15y/100 - 5x/100
Given, total gain  = 70
So,
15y/100 - 5x/100=70
15y - 5x = 7000
Dividing it by 5, we get
3y - x = 1400 
-x + 3y = 1400...........(1)
If he sells the tea set at 5 % gain and lemon set at 10 % gain, he gains Rs 130.
Therefore, using same steps as above, gain is given as ,
5x/100 + 10y/100 = 130
5x + 10y = 13000
Dividing it by 5, we get
x + 2y = 2600 ..............(2)
Adding (1) and (2), we get

- x + 3y = 1400
  x + 2y = 2600
______________
      5y = 4000
______________
y = 4000/5
y = 800
Substituting the value of y = 800 in (2), we get
x + 2y = 2600
x + 2*800 = 2600
x + 2600 - 1600 
x = 1000
So the cost price of tea set is Rs 1000 and the cost price of lemon set is Rs 800.


 

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