Question

On selling a tea set at 5% loss and lemon set at 15% gain a crockery seller gain rupees 7. if he sells the tea set at 5% gain and lemon set at 10% gain he gains rupees 13 find the actual price of the tea set and the lemon set

Answer 1

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 = 7
15y - 5x = 700
Dividing it by 5, we get
3y - x = 140
-x + 3y = 140...........(1)
If he sells the tea set at 5 % gain and lemon set at 10 % gain, he gains Rs 13.
Therefore,
5x/100 + 10y/100 = 13
5x + 10y = 1300
Dividing it by 5, we get
x + 2y = 260 ..............(2)
Adding (1) and (2), we get

- x + 3y = 140
x + 2y = 260
______________
5y = 400
______________
y = 400/5
y = 80
Substituting the value of y = 80 in (2), we get
x + 2y = 260
x + 2*800 = 260
x + 2600 - 160
x = 100
So the cost price of tea set is Rs 100 and the cost price of lemon set is Rs 80.