on selling a tea–set at 5% loss and a glass set at 10% gain, a crockery seller gains Rs 8. If he sells the tea–set at gain of 5% and glass set at 15% gain, he gains Rs 15. Find the actual price of the tea–set and glass set.
Let the cost price of the tea–set is x and glass set is y.
Case 1: Tea–set at 5% loss and a glass set at 10% gain.
Loss on tea–set = 
Gain on glass set = 
∴ Net gain = 
⇒ 2y – x = 160 …. (1)
x = 2y – 160
Case 2: Tea–set at gain of 5% and glass set at 15% gain.
gain on tea–set = 
Gain on glass set = 
∴ Net gain = 
⇒ 5x + 6y = 1500 … (2)
Put value of x in (2) to get,
5(2y – 160) + 6y = 1500
10y – 800 + 6y = 1500
16 y = 1500 + 800
16 y = 2300
y = Rs 143.75
Put the value of y in (1) to get,
2(143.75) – x = 160
287.5 – x = 160
x = Rs 127.5
Hence the cost price of the tea–set is Rs 127.5 and glass set is Rs 143.75.
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