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If two is added to both tge numerator and the denominator of a fraction,the fraction becomes 3/4. If 3 is substracted from both the numerator and the denominator of the fraction,it becomes 2/3. What is the value of fraction?
Most Upvoted Answer
If two is added to both tge numerator and the denominator of a fractio...
Given:
Let the fraction be represented as x/y.
Adding 2 to both the numerator and the denominator:
(x + 2)/(y + 2) = 3/4
Subtracting 3 from both the numerator and the denominator:
(x - 3)/(y - 3) = 2/3
Approach:
To solve this problem, we will use the method of simultaneous equations. We will solve the given equations to find the values of x and y.
Solution:
Step 1: Simplify the equations
(x + 2)/(y + 2) = 3/4
Cross-multiplying, we get:
4(x + 2) = 3(y + 2)
(x - 3)/(y - 3) = 2/3
Cross-multiplying, we get:
3(x - 3) = 2(y - 3)
Step 2: Expand and simplify the equations
4x + 8 = 3y + 6 ...(1)
3x - 9 = 2y - 6 ...(2)
Step 3: Rearrange the equations
4x - 3y = -2 ...(3)
3x - 2y = 3 ...(4)
Step 4: Multiply equation (3) by 2 and equation (4) by 3 to eliminate the y term
8x - 6y = -4 ...(5)
9x - 6y = 9 ...(6)
Step 5: Subtract equation (5) from equation (6)
9x - 8x = 9 - (-4)
x = 13
Step 6: Substitute the value of x in equation (3)
4(13) - 3y = -2
52 - 3y = -2
-3y = -54
y = 18
Step 7: Verify the solution
Substituting the values of x and y in the original equations:
(x + 2)/(y + 2) = 3/4
(13 + 2)/(18 + 2) = 3/4
15/20 = 3/4
3/4 = 3/4
(x - 3)/(y - 3) = 2/3
(13 - 3)/(18 - 3) = 2/3
10/15 = 2/3
2/3 = 2/3
Hence, the value of the fraction is 13/18.
Let the fraction be represented as x/y.
Adding 2 to both the numerator and the denominator:
(x + 2)/(y + 2) = 3/4
Subtracting 3 from both the numerator and the denominator:
(x - 3)/(y - 3) = 2/3
Approach:
To solve this problem, we will use the method of simultaneous equations. We will solve the given equations to find the values of x and y.
Solution:
Step 1: Simplify the equations
(x + 2)/(y + 2) = 3/4
Cross-multiplying, we get:
4(x + 2) = 3(y + 2)
(x - 3)/(y - 3) = 2/3
Cross-multiplying, we get:
3(x - 3) = 2(y - 3)
Step 2: Expand and simplify the equations
4x + 8 = 3y + 6 ...(1)
3x - 9 = 2y - 6 ...(2)
Step 3: Rearrange the equations
4x - 3y = -2 ...(3)
3x - 2y = 3 ...(4)
Step 4: Multiply equation (3) by 2 and equation (4) by 3 to eliminate the y term
8x - 6y = -4 ...(5)
9x - 6y = 9 ...(6)
Step 5: Subtract equation (5) from equation (6)
9x - 8x = 9 - (-4)
x = 13
Step 6: Substitute the value of x in equation (3)
4(13) - 3y = -2
52 - 3y = -2
-3y = -54
y = 18
Step 7: Verify the solution
Substituting the values of x and y in the original equations:
(x + 2)/(y + 2) = 3/4
(13 + 2)/(18 + 2) = 3/4
15/20 = 3/4
3/4 = 3/4
(x - 3)/(y - 3) = 2/3
(13 - 3)/(18 - 3) = 2/3
10/15 = 2/3
2/3 = 2/3
Hence, the value of the fraction is 13/18.
Community Answer
If two is added to both tge numerator and the denominator of a fractio...
13/18. 15/20=3/4, 10/15=2/3.
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If two is added to both tge numerator and the denominator of a fraction,the fraction becomes 3/4. If 3 is substracted from both the numerator and the denominator of the fraction,it becomes 2/3. What is the value of fraction?
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If two is added to both tge numerator and the denominator of a fraction,the fraction becomes 3/4. If 3 is substracted from both the numerator and the denominator of the fraction,it becomes 2/3. What is the value of fraction? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If two is added to both tge numerator and the denominator of a fraction,the fraction becomes 3/4. If 3 is substracted from both the numerator and the denominator of the fraction,it becomes 2/3. What is the value of fraction? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If two is added to both tge numerator and the denominator of a fraction,the fraction becomes 3/4. If 3 is substracted from both the numerator and the denominator of the fraction,it becomes 2/3. What is the value of fraction?.
If two is added to both tge numerator and the denominator of a fraction,the fraction becomes 3/4. If 3 is substracted from both the numerator and the denominator of the fraction,it becomes 2/3. What is the value of fraction? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If two is added to both tge numerator and the denominator of a fraction,the fraction becomes 3/4. If 3 is substracted from both the numerator and the denominator of the fraction,it becomes 2/3. What is the value of fraction? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If two is added to both tge numerator and the denominator of a fraction,the fraction becomes 3/4. If 3 is substracted from both the numerator and the denominator of the fraction,it becomes 2/3. What is the value of fraction?.
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