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On selling a tea set at 5% loss and lemon set at 15% gain a crockery seller gains rupees 7 . if he sells tea set at 5% gain and the lemon set at 10% gain , he gain rupees 13 find the actual price of the tea set and the lemon set.?
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Problem: On selling a tea set at 5% loss and lemon set at 15% gain a crockery seller gains rupees 7. If he sells tea set at 5% gain and the lemon set at 10% gain, he gains rupees 13. Find the actual price of the tea set and the lemon set.
Solution:
Let the cost price of the tea set be x and the cost price of the lemon set be y.
First Case:
When tea set is sold at 5% loss and lemon set is sold at 15% gain, the seller gains Rs. 7.
Selling price of tea set = 0.95x (as it is sold at 5% loss)
Selling price of lemon set = 1.15y (as it is sold at 15% gain)
Total gain = Selling price of tea set + Selling price of lemon set - (Cost price of tea set + Cost price of lemon set)
= 0.95x + 1.15y - (x+y)
= -0.05x + 0.15y + 7
As per the question, Total gain = Rs. 7
So, -0.05x + 0.15y + 7 = 7
=> -0.05x + 0.15y = 0
Second Case:
When tea set is sold at 5% gain and lemon set is sold at 10% gain, the seller gains Rs. 13.
Selling price of tea set = 1.05x (as it is sold at 5% gain)
Selling price of lemon set = 1.1y (as it is sold at 10% gain)
Total gain = Selling price of tea set + Selling price of lemon set - (Cost price of tea set + Cost price of lemon set)
= 1.05x + 1.1y - (x+y)
= 0.05x + 0.1y + 13
As per the question, Total gain = Rs. 13
So, 0.05x + 0.1y + 13 = 13
=> 0.05x + 0.1y = 0
Solving Equations:
We have two equations from the above cases:
-0.05x + 0.15y = 0
0.05x + 0.1y = 0
On solving these equations, we get:
y = 3x (Multiplying first equation by 3 and adding it to second equation)
Substituting y = 3x in any of the above equations, we get:
-0.05x + 0.15(3x) = 0
=> 0.4x = 0
=> x = 0
This means that the cost price of the tea set is zero, which is not possible. Hence, this problem has no solution.
Conclusion:
After solving the equations, we found that the problem has no solution. This means that the given information is inconsistent and cannot be solved.
Solution:
Let the cost price of the tea set be x and the cost price of the lemon set be y.
First Case:
When tea set is sold at 5% loss and lemon set is sold at 15% gain, the seller gains Rs. 7.
Selling price of tea set = 0.95x (as it is sold at 5% loss)
Selling price of lemon set = 1.15y (as it is sold at 15% gain)
Total gain = Selling price of tea set + Selling price of lemon set - (Cost price of tea set + Cost price of lemon set)
= 0.95x + 1.15y - (x+y)
= -0.05x + 0.15y + 7
As per the question, Total gain = Rs. 7
So, -0.05x + 0.15y + 7 = 7
=> -0.05x + 0.15y = 0
Second Case:
When tea set is sold at 5% gain and lemon set is sold at 10% gain, the seller gains Rs. 13.
Selling price of tea set = 1.05x (as it is sold at 5% gain)
Selling price of lemon set = 1.1y (as it is sold at 10% gain)
Total gain = Selling price of tea set + Selling price of lemon set - (Cost price of tea set + Cost price of lemon set)
= 1.05x + 1.1y - (x+y)
= 0.05x + 0.1y + 13
As per the question, Total gain = Rs. 13
So, 0.05x + 0.1y + 13 = 13
=> 0.05x + 0.1y = 0
Solving Equations:
We have two equations from the above cases:
-0.05x + 0.15y = 0
0.05x + 0.1y = 0
On solving these equations, we get:
y = 3x (Multiplying first equation by 3 and adding it to second equation)
Substituting y = 3x in any of the above equations, we get:
-0.05x + 0.15(3x) = 0
=> 0.4x = 0
=> x = 0
This means that the cost price of the tea set is zero, which is not possible. Hence, this problem has no solution.
Conclusion:
After solving the equations, we found that the problem has no solution. This means that the given information is inconsistent and cannot be solved.
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On selling a tea set at 5% loss and lemon set at 15% gain a crockery seller gains rupees 7 . if he sells tea set at 5% gain and the lemon set at 10% gain , he gain rupees 13 find the actual price of the tea set and the lemon set.?
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On selling a tea set at 5% loss and lemon set at 15% gain a crockery seller gains rupees 7 . if he sells tea set at 5% gain and the lemon set at 10% gain , he gain rupees 13 find the actual price of the tea set and the lemon set.? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about On selling a tea set at 5% loss and lemon set at 15% gain a crockery seller gains rupees 7 . if he sells tea set at 5% gain and the lemon set at 10% gain , he gain rupees 13 find the actual price of the tea set and the lemon set.? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for On selling a tea set at 5% loss and lemon set at 15% gain a crockery seller gains rupees 7 . if he sells tea set at 5% gain and the lemon set at 10% gain , he gain rupees 13 find the actual price of the tea set and the lemon set.?.
On selling a tea set at 5% loss and lemon set at 15% gain a crockery seller gains rupees 7 . if he sells tea set at 5% gain and the lemon set at 10% gain , he gain rupees 13 find the actual price of the tea set and the lemon set.? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about On selling a tea set at 5% loss and lemon set at 15% gain a crockery seller gains rupees 7 . if he sells tea set at 5% gain and the lemon set at 10% gain , he gain rupees 13 find the actual price of the tea set and the lemon set.? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for On selling a tea set at 5% loss and lemon set at 15% gain a crockery seller gains rupees 7 . if he sells tea set at 5% gain and the lemon set at 10% gain , he gain rupees 13 find the actual price of the tea set and the lemon set.?.
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