On selling a tea-set 5% loss and a lemon-set at 15% gain, a crockery seller gains Rs. 7. If he sells the tea-set at 5% gain and the lemon-set at 10% gain, he gains Rs. 13. Find the actual price of the tea-set and the lemon-set.

Explanation

Let the cost price of the tea-set and 15% gain on lemon-set
Loss on tea-set = Rs. `(5x)/(100)`
Gain on lemon-set = Rs `(15y)/(100)`
But net gain = Rs. 7
implies `(15y)/(100) - (5x)/(100) = 7 implies 15y - 5x = 700 implies -x + 3y = 140 " ...(1)"`
Case II : When 5% gain on tea-set and 10% gain on lemon-set
Gain on tea-set = Rs. `(5x)/(100)`
Gain on lemon-set = Rs. `(10 y)/(100)`
But net gain = Rs. 13
implies `(5x)/(100) + (10y)/(100) = 13 implies 5x + 10y = 1300 implies x + 2y = 260 " ...(2)"`
Adding equations (1) and (2), we get
5y = 400 implies y = 80
Putting y = 80 in equation (1), we get
x = 3 (80) - 140 = 100
`therefore` Cost of tea-set = Rs. 100 and the cost of lemon-set = Rs. 80