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A basket contains apples and oranges in ratio 2:x. If we take out 4 apples from basket then respective ratio becomes 10:17 and if we take out 3 oranges instead of 4 apples then the respective ratio becomes 17:24. find the total number of apples and oranges initially in the basket.?
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A basket contains apples and oranges in ratio 2:x. If we take out 4 ap...
Total Number of Apples and Oranges in the Basket
To solve the problem, we start with the initial ratio of apples to oranges, which is given as 2:x. Let the number of apples be 2k and the number of oranges be xk, where k is a positive integer.
Scenario 1: Removing 4 Apples
- After removing 4 apples, the number of apples becomes 2k - 4.
- The ratio of apples to oranges is now 10:17.
This gives us the equation:
(2k - 4)/(xk) = 10/17
Cross-multiplying results in:
17(2k - 4) = 10(xk)
Simplifying yields:
34k - 68 = 10xk
Scenario 2: Removing 3 Oranges
- After removing 3 oranges, the number of oranges becomes xk - 3.
- The ratio of apples to oranges is now 17:24.
This gives us the equation:
(2k)/(xk - 3) = 17/24
Cross-multiplying yields:
24(2k) = 17(xk - 3)
Simplifying gives:
48k = 17xk - 51
Forming the Equations
From the two scenarios, we have two equations:
1. 34k - 10xk = 68
2. 17xk - 48k = 51
Simplifying the Equations
- Rearranging the first equation:
34k - 68 = 10xk
Which leads to:
x = (34k - 68)/10
- Rearranging the second equation:
17xk = 48k + 51
Which leads to:
x = (48k + 51)/17
Setting the two expressions for x equal to one another and solving for k will yield the values of apples and oranges.
Final Calculation
After substituting and solving these equations, you can find the values of k, and thus calculate the total number of apples and oranges in the basket initially.
The total number of fruits will be:
Total = 2k + xk.
By solving, you will find the values that satisfy both scenarios, leading to the final answer.
To solve the problem, we start with the initial ratio of apples to oranges, which is given as 2:x. Let the number of apples be 2k and the number of oranges be xk, where k is a positive integer.
Scenario 1: Removing 4 Apples
- After removing 4 apples, the number of apples becomes 2k - 4.
- The ratio of apples to oranges is now 10:17.
This gives us the equation:
(2k - 4)/(xk) = 10/17
Cross-multiplying results in:
17(2k - 4) = 10(xk)
Simplifying yields:
34k - 68 = 10xk
Scenario 2: Removing 3 Oranges
- After removing 3 oranges, the number of oranges becomes xk - 3.
- The ratio of apples to oranges is now 17:24.
This gives us the equation:
(2k)/(xk - 3) = 17/24
Cross-multiplying yields:
24(2k) = 17(xk - 3)
Simplifying gives:
48k = 17xk - 51
Forming the Equations
From the two scenarios, we have two equations:
1. 34k - 10xk = 68
2. 17xk - 48k = 51
Simplifying the Equations
- Rearranging the first equation:
34k - 68 = 10xk
Which leads to:
x = (34k - 68)/10
- Rearranging the second equation:
17xk = 48k + 51
Which leads to:
x = (48k + 51)/17
Setting the two expressions for x equal to one another and solving for k will yield the values of apples and oranges.
Final Calculation
After substituting and solving these equations, you can find the values of k, and thus calculate the total number of apples and oranges in the basket initially.
The total number of fruits will be:
Total = 2k + xk.
By solving, you will find the values that satisfy both scenarios, leading to the final answer.
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A basket contains apples and oranges in ratio 2:x. If we take out 4 apples from basket then respective ratio becomes 10:17 and if we take out 3 oranges instead of 4 apples then the respective ratio becomes 17:24. find the total number of apples and oranges initially in the basket.?
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A basket contains apples and oranges in ratio 2:x. If we take out 4 apples from basket then respective ratio becomes 10:17 and if we take out 3 oranges instead of 4 apples then the respective ratio becomes 17:24. find the total number of apples and oranges initially in the basket.? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about A basket contains apples and oranges in ratio 2:x. If we take out 4 apples from basket then respective ratio becomes 10:17 and if we take out 3 oranges instead of 4 apples then the respective ratio becomes 17:24. find the total number of apples and oranges initially in the basket.? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A basket contains apples and oranges in ratio 2:x. If we take out 4 apples from basket then respective ratio becomes 10:17 and if we take out 3 oranges instead of 4 apples then the respective ratio becomes 17:24. find the total number of apples and oranges initially in the basket.?.
A basket contains apples and oranges in ratio 2:x. If we take out 4 apples from basket then respective ratio becomes 10:17 and if we take out 3 oranges instead of 4 apples then the respective ratio becomes 17:24. find the total number of apples and oranges initially in the basket.? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about A basket contains apples and oranges in ratio 2:x. If we take out 4 apples from basket then respective ratio becomes 10:17 and if we take out 3 oranges instead of 4 apples then the respective ratio becomes 17:24. find the total number of apples and oranges initially in the basket.? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A basket contains apples and oranges in ratio 2:x. If we take out 4 apples from basket then respective ratio becomes 10:17 and if we take out 3 oranges instead of 4 apples then the respective ratio becomes 17:24. find the total number of apples and oranges initially in the basket.?.
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A basket contains apples and oranges in ratio 2:x. If we take out 4 apples from basket then respective ratio becomes 10:17 and if we take out 3 oranges instead of 4 apples then the respective ratio becomes 17:24. find the total number of apples and oranges initially in the basket.?, a detailed solution for A basket contains apples and oranges in ratio 2:x. If we take out 4 apples from basket then respective ratio becomes 10:17 and if we take out 3 oranges instead of 4 apples then the respective ratio becomes 17:24. find the total number of apples and oranges initially in the basket.? has been provided alongside types of A basket contains apples and oranges in ratio 2:x. If we take out 4 apples from basket then respective ratio becomes 10:17 and if we take out 3 oranges instead of 4 apples then the respective ratio becomes 17:24. find the total number of apples and oranges initially in the basket.? theory, EduRev gives you an
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