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

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

Doubt by Myank (2021) & Samriddhi (2023)

Solution: 
Let the actual price of Tea Set = Rs x
and the actual price of Lemon Set = Rs y
ATQ
5% loss on Tea Set + 15% gain on Lemon Set = 7
-5x/100 + 15y/100 = 7
-x/20+3y/20=7
(-x+3y)/20=7
-x+3y=140 — (1)

5% gain on Tea Set + 10% gain on Lemon Set = 13
5x/100+10y/100 = 13
x/20 + 1y/10 = 13
x/20 + 2y/20 = 13
(x+2y)/20 = 13
x+2y = 260 — (2)

Adding equation (1) and (2)

-x+3y=140
 x+2y = 260
--------------------
0+5y=400
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5y = 400
y= 400/5
y = 80

putting in eq(1)
-x+3y=140
-x+3(80)=140
-x+240=140
-x=140-240
-x=-100
x=100

Therefore,
The actual price of Tea Set = Rs 100
and the actual price of Lemon Set = Rs 80