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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