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# On selling a tea-set at 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

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This is the basic and exam oriented question from linear equations in two variables in which we have to the cost price of a tea set and a lemon set if it is given that on selling a tea-set at 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.

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 3E, question no 46

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1. Let the cost price of the tea-set and the lemon-set be Rs x and Rs y respectively.

CaseI:  When tea set is sold at 5% loss and lemon-set at 15% gain.

Loss in tea-set = Rs. 5x/100 = Rs. x/20

Gain on lemon-set = Rs. 15y/100 = Rs. 3y/20

Net gain = Rs. 3y/20x/20

3y/20x​/20=7

3yx=140

x3y+140=0 (i)

CaseII:  When tea-set is sold at 5% gain and the lemon-set at 10% gain.

Gain on tea-set = Rs. 5x​/100 = Rs. x/20

Gain on lemon-set = Rs. 10y/100= Rs. y/10

Total gain = Rs. x​/20+y/10

x​/20+y​/10=13

x+2y=260

x+2y260=0 .(ii)

Subtracting equation (ii) from equation (i), we get
5y+400=0y=80

Putting y=80 in equation (i), we get
x240+140=0
x=100

Hence, the cost prices of tea-set and lemon-set are Rs. 100 and Rs. 80 respectively.

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