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On selling a tea-set at 5% loss and lemonset at 15% gain, a crockery seller gains ₹ 7. If he sells the tea-set at 5% gain and the lemon-set at 10% gain, he gains ₹ 13. Find the actual prices of the tea-set and the lemon-set.
- a)₹ 100, ₹ 80
- b)₹ 90, ₹ 100
- c)₹ 120, ₹ 60
- d)₹ 150, ₹ 80
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
On selling a tea-set at 5% loss and lemonset at 15% gain, a crockery s...
Let's assume the cost price of the tea-set is x and the cost price of the lemon-set is y.
Selling at Loss and Gain
When the tea-set is sold at a 5% loss, the selling price becomes 0.95x. On the other hand, when the lemon-set is sold at a 15% gain, the selling price becomes 1.15y. The total gain from these sales is 7.
Selling at Gain and Gain
When the tea-set is sold at a 5% gain, the selling price becomes 1.05x. Similarly, when the lemon-set is sold at a 10% gain, the selling price becomes 1.10y. The total gain from these sales is 13.
Forming Equations
We can form the following equations based on the given information:
0.95x + 1.15y = x + y + 7 (Equation 1)
1.05x + 1.10y = x + y + 13 (Equation 2)
Simplifying the Equations
We can simplify Equation 1 by subtracting x and y from both sides:
0.95x - x + 1.15y - y = 7
-0.05x + 0.15y = 7 (Equation 3)
Similarly, we can simplify Equation 2 by subtracting x and y from both sides:
1.05x - x + 1.10y - y = 13
0.05x + 0.10y = 13 (Equation 4)
Solving the Equations
Now, we can solve Equations 3 and 4 simultaneously to find the values of x and y.
Multiplying Equation 3 by 20 and Equation 4 by 100 to eliminate decimals:
-1x + 3y = 140 (Equation 5)
5x + 10y = 1300 (Equation 6)
Multiplying Equation 5 by 5 and Equation 6 by 1 to make the coefficients of x equal:
-5x + 15y = 700 (Equation 7)
5x + 10y = 1300 (Equation 6)
Adding Equations 7 and 6:
25y = 2000
y = 80
Substituting the value of y in Equation 5:
-1x + 3(80) = 140
-1x + 240 = 140
-1x = -100
x = 100
Therefore, the cost price of the tea-set is 100 and the cost price of the lemon-set is 80. Thus, option A is correct.
Selling at Loss and Gain
When the tea-set is sold at a 5% loss, the selling price becomes 0.95x. On the other hand, when the lemon-set is sold at a 15% gain, the selling price becomes 1.15y. The total gain from these sales is 7.
Selling at Gain and Gain
When the tea-set is sold at a 5% gain, the selling price becomes 1.05x. Similarly, when the lemon-set is sold at a 10% gain, the selling price becomes 1.10y. The total gain from these sales is 13.
Forming Equations
We can form the following equations based on the given information:
0.95x + 1.15y = x + y + 7 (Equation 1)
1.05x + 1.10y = x + y + 13 (Equation 2)
Simplifying the Equations
We can simplify Equation 1 by subtracting x and y from both sides:
0.95x - x + 1.15y - y = 7
-0.05x + 0.15y = 7 (Equation 3)
Similarly, we can simplify Equation 2 by subtracting x and y from both sides:
1.05x - x + 1.10y - y = 13
0.05x + 0.10y = 13 (Equation 4)
Solving the Equations
Now, we can solve Equations 3 and 4 simultaneously to find the values of x and y.
Multiplying Equation 3 by 20 and Equation 4 by 100 to eliminate decimals:
-1x + 3y = 140 (Equation 5)
5x + 10y = 1300 (Equation 6)
Multiplying Equation 5 by 5 and Equation 6 by 1 to make the coefficients of x equal:
-5x + 15y = 700 (Equation 7)
5x + 10y = 1300 (Equation 6)
Adding Equations 7 and 6:
25y = 2000
y = 80
Substituting the value of y in Equation 5:
-1x + 3(80) = 140
-1x + 240 = 140
-1x = -100
x = 100
Therefore, the cost price of the tea-set is 100 and the cost price of the lemon-set is 80. Thus, option A is correct.
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Community Answer
On selling a tea-set at 5% loss and lemonset at 15% gain, a crockery s...
Let cost price of tea-set = ₹ x
and cost price of lemon-set = ₹ y
(i) Loss on tea-set =
Gain on lemon-set =
Also,
...(1)
(ii) Gain on tea-set =
Gain on lemon-set =
Also,
..(2)
Solving (1) and (2), we get ⇒ y = ₹ 80 and x = ₹ 100
and cost price of lemon-set = ₹ y
(i) Loss on tea-set =
Gain on lemon-set =
Also,
...(1)(ii) Gain on tea-set =
Gain on lemon-set =
Also,
..(2)Solving (1) and (2), we get ⇒ y = ₹ 80 and x = ₹ 100
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On selling a tea-set at 5% loss and lemonset at 15% gain, a crockery seller gains 7. If he sells the tea-set at 5% gain and the lemon-set at 10% gain, he gains 13. Find the actual prices of the tea-set and the lemon-set.a) 100, 80b) 90, 100c) 120, 60d) 150, 80Correct answer is option 'A'. Can you explain this answer?
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On selling a tea-set at 5% loss and lemonset at 15% gain, a crockery seller gains 7. If he sells the tea-set at 5% gain and the lemon-set at 10% gain, he gains 13. Find the actual prices of the tea-set and the lemon-set.a) 100, 80b) 90, 100c) 120, 60d) 150, 80Correct answer is option 'A'. Can you explain this answer? for Class 10 2024 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 lemonset at 15% gain, a crockery seller gains 7. If he sells the tea-set at 5% gain and the lemon-set at 10% gain, he gains 13. Find the actual prices of the tea-set and the lemon-set.a) 100, 80b) 90, 100c) 120, 60d) 150, 80Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for On selling a tea-set at 5% loss and lemonset at 15% gain, a crockery seller gains 7. If he sells the tea-set at 5% gain and the lemon-set at 10% gain, he gains 13. Find the actual prices of the tea-set and the lemon-set.a) 100, 80b) 90, 100c) 120, 60d) 150, 80Correct answer is option 'A'. Can you explain this answer?.
On selling a tea-set at 5% loss and lemonset at 15% gain, a crockery seller gains 7. If he sells the tea-set at 5% gain and the lemon-set at 10% gain, he gains 13. Find the actual prices of the tea-set and the lemon-set.a) 100, 80b) 90, 100c) 120, 60d) 150, 80Correct answer is option 'A'. Can you explain this answer? for Class 10 2024 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 lemonset at 15% gain, a crockery seller gains 7. If he sells the tea-set at 5% gain and the lemon-set at 10% gain, he gains 13. Find the actual prices of the tea-set and the lemon-set.a) 100, 80b) 90, 100c) 120, 60d) 150, 80Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for On selling a tea-set at 5% loss and lemonset at 15% gain, a crockery seller gains 7. If he sells the tea-set at 5% gain and the lemon-set at 10% gain, he gains 13. Find the actual prices of the tea-set and the lemon-set.a) 100, 80b) 90, 100c) 120, 60d) 150, 80Correct answer is option 'A'. Can you explain this answer?.
Solutions for On selling a tea-set at 5% loss and lemonset at 15% gain, a crockery seller gains 7. If he sells the tea-set at 5% gain and the lemon-set at 10% gain, he gains 13. Find the actual prices of the tea-set and the lemon-set.a) 100, 80b) 90, 100c) 120, 60d) 150, 80Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10.
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On selling a tea-set at 5% loss and lemonset at 15% gain, a crockery seller gains 7. If he sells the tea-set at 5% gain and the lemon-set at 10% gain, he gains 13. Find the actual prices of the tea-set and the lemon-set.a) 100, 80b) 90, 100c) 120, 60d) 150, 80Correct answer is option 'A'. Can you explain this answer?, a detailed solution for On selling a tea-set at 5% loss and lemonset at 15% gain, a crockery seller gains 7. If he sells the tea-set at 5% gain and the lemon-set at 10% gain, he gains 13. Find the actual prices of the tea-set and the lemon-set.a) 100, 80b) 90, 100c) 120, 60d) 150, 80Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of On selling a tea-set at 5% loss and lemonset at 15% gain, a crockery seller gains 7. If he sells the tea-set at 5% gain and the lemon-set at 10% gain, he gains 13. Find the actual prices of the tea-set and the lemon-set.a) 100, 80b) 90, 100c) 120, 60d) 150, 80Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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