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A person bought two bicycles for Rs. 1600 and sold the first at 10% profit and the second at 20% profit. If he sold the first at 20% profit and the second at 10% profit, he would get 5 Rs. more. The difference in the cost price of the two bicycles was:
Correct answer is '50'. Can you explain this answer?
Most Upvoted Answer
A person bought two bicycles for Rs. 1600 and sold the first at 10% p...
Total cost price Rs. 1600 Let CP1 = 600 and CP2 = 1000
Case I, When he sells first at 10% profit and second at 20% profit:
∴ Profit on CP1 = 10% on 600 = Rs. 60
Profit on CP2 = 20% on 1000 = Rs. 200
Total Profit = ₹ 260 ...(i) Case II, When he sells first at 20% profit and second at 10% profit:
∴ Profit on CP1 = 20% on 600 = Rs. 120
Profit on 2 = 10% on 1000 = Rs. 100
Total Profit = Rs. 220...(ii)
Difference in Profit [(i)−(ii)} = 260 − 220 Rs.
= Rs. 40
When difference in profit is Rs. 40, then difference in cost price would be Rs. (1000 − 600) = Rs. 400.
When difference in profit is Rs. 5, then difference in cost price would be:
Rs. =((400/40) × 5)
= Rs. 50.
Hence, the correct answer is 50.
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A person bought two bicycles for Rs. 1600 and sold the first at 10% p...
Given:
- The person bought two bicycles for Rs. 1600.
- The first bicycle was sold at a 10% profit.
- The second bicycle was sold at a 20% profit.
- If the person sold the first bicycle at a 20% profit and the second bicycle at a 10% profit, they would get Rs. 5 more.
To find:
The difference in the cost price of the two bicycles.
Assumption:
Let the cost price of the first bicycle be x and the cost price of the second bicycle be y.
Solution:
Case 1: Selling the first bicycle with a 10% profit and the second bicycle with a 20% profit.
- Selling price of the first bicycle = x + 10% of x = 1.1x
- Selling price of the second bicycle = y + 20% of y = 1.2y
- Total selling price = Rs. 1600
- Equation 1: 1.1x + 1.2y = 1600
Case 2: Selling the first bicycle with a 20% profit and the second bicycle with a 10% profit (getting Rs. 5 more).
- Selling price of the first bicycle = x + 20% of x = 1.2x
- Selling price of the second bicycle = y + 10% of y = 1.1y
- Total selling price = Rs. 1600 + Rs. 5 = Rs. 1605
- Equation 2: 1.2x + 1.1y = 1605
Solving the Equations:
We have two equations:
1.1x + 1.2y = 1600
1.2x + 1.1y = 1605
To eliminate decimals, we can multiply both equations by 10:
11x + 12y = 16000
12x + 11y = 16050
Multiplying the first equation by 12 and the second equation by 11:
132x + 144y = 192000
132x + 121y = 176550
Subtracting the second equation from the first equation:
(132x + 144y) - (132x + 121y) = 192000 - 176550
23y = 15450
y = 15450/23
y = 670
Substituting the value of y in Equation 1:
1.1x + 1.2(670) = 1600
1.1x + 804 = 1600
1.1x = 1600 - 804
1.1x = 796
x = 796/1.1
x = 724
The cost price of the first bicycle (x) is Rs. 724 and the cost price of the second bicycle (y) is Rs. 670.
Calculating the difference in cost price:
Difference in cost price = x - y = 724 - 670 = Rs. 54
Therefore, the difference in the cost price of the two bicycles is Rs. 54.
- The person bought two bicycles for Rs. 1600.
- The first bicycle was sold at a 10% profit.
- The second bicycle was sold at a 20% profit.
- If the person sold the first bicycle at a 20% profit and the second bicycle at a 10% profit, they would get Rs. 5 more.
To find:
The difference in the cost price of the two bicycles.
Assumption:
Let the cost price of the first bicycle be x and the cost price of the second bicycle be y.
Solution:
Case 1: Selling the first bicycle with a 10% profit and the second bicycle with a 20% profit.
- Selling price of the first bicycle = x + 10% of x = 1.1x
- Selling price of the second bicycle = y + 20% of y = 1.2y
- Total selling price = Rs. 1600
- Equation 1: 1.1x + 1.2y = 1600
Case 2: Selling the first bicycle with a 20% profit and the second bicycle with a 10% profit (getting Rs. 5 more).
- Selling price of the first bicycle = x + 20% of x = 1.2x
- Selling price of the second bicycle = y + 10% of y = 1.1y
- Total selling price = Rs. 1600 + Rs. 5 = Rs. 1605
- Equation 2: 1.2x + 1.1y = 1605
Solving the Equations:
We have two equations:
1.1x + 1.2y = 1600
1.2x + 1.1y = 1605
To eliminate decimals, we can multiply both equations by 10:
11x + 12y = 16000
12x + 11y = 16050
Multiplying the first equation by 12 and the second equation by 11:
132x + 144y = 192000
132x + 121y = 176550
Subtracting the second equation from the first equation:
(132x + 144y) - (132x + 121y) = 192000 - 176550
23y = 15450
y = 15450/23
y = 670
Substituting the value of y in Equation 1:
1.1x + 1.2(670) = 1600
1.1x + 804 = 1600
1.1x = 1600 - 804
1.1x = 796
x = 796/1.1
x = 724
The cost price of the first bicycle (x) is Rs. 724 and the cost price of the second bicycle (y) is Rs. 670.
Calculating the difference in cost price:
Difference in cost price = x - y = 724 - 670 = Rs. 54
Therefore, the difference in the cost price of the two bicycles is Rs. 54.
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A person bought two bicycles for Rs. 1600 and sold the first at 10% profit and the second at 20% profit. If he sold the first at 20% profit and the second at 10% profit, he would get 5 Rs. more. The difference in the cost price of the two bicycles was:Correct answer is '50'. Can you explain this answer?
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A person bought two bicycles for Rs. 1600 and sold the first at 10% profit and the second at 20% profit. If he sold the first at 20% profit and the second at 10% profit, he would get 5 Rs. more. The difference in the cost price of the two bicycles was:Correct answer is '50'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A person bought two bicycles for Rs. 1600 and sold the first at 10% profit and the second at 20% profit. If he sold the first at 20% profit and the second at 10% profit, he would get 5 Rs. more. The difference in the cost price of the two bicycles was:Correct answer is '50'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A person bought two bicycles for Rs. 1600 and sold the first at 10% profit and the second at 20% profit. If he sold the first at 20% profit and the second at 10% profit, he would get 5 Rs. more. The difference in the cost price of the two bicycles was:Correct answer is '50'. Can you explain this answer?.
A person bought two bicycles for Rs. 1600 and sold the first at 10% profit and the second at 20% profit. If he sold the first at 20% profit and the second at 10% profit, he would get 5 Rs. more. The difference in the cost price of the two bicycles was:Correct answer is '50'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A person bought two bicycles for Rs. 1600 and sold the first at 10% profit and the second at 20% profit. If he sold the first at 20% profit and the second at 10% profit, he would get 5 Rs. more. The difference in the cost price of the two bicycles was:Correct answer is '50'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A person bought two bicycles for Rs. 1600 and sold the first at 10% profit and the second at 20% profit. If he sold the first at 20% profit and the second at 10% profit, he would get 5 Rs. more. The difference in the cost price of the two bicycles was:Correct answer is '50'. Can you explain this answer?.
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