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If z varies directly as x and inversely as y find the percentage increase in z due to an increase of 12% in x and a decrease of 20% in y ?
Verified Answer
If z varies directly as x and inversely as y find the percentage incre...
Given Z varies directly as x and inversely as y.
Hence Z = (X/Y), Assuming proportionately constant as 1
X is increased by 12 % and Y is decreased by 20 %
Hence value of Z becomes,
Z = 1.12x/0.8y
Z = 112x/80y
Change in value of Z = (112X/80Y) - (X/Y)
= 32X/80Y
Increase in Z's percentage = (32X/80Y) � (X/Y) � 100
= (32X/80y) � (Y/X) � 100
= 40 %
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Most Upvoted Answer
If z varies directly as x and inversely as y find the percentage incre...
Understanding the Relationship
When z varies directly as x and inversely as y, we can express this relationship mathematically as:
z = k * (x/y)
where k is a constant.
Initial Changes in Variables
To find the percentage change in z due to changes in x and y:
- An increase of 12% in x means:
- New x = x + 0.12x = 1.12x
- A decrease of 20% in y means:
- New y = y - 0.20y = 0.80y
Calculating the New Value of z
Substituting the new values of x and y into the equation for z:
- New z = k * (1.12x / 0.80y)
Simplifying this, we get:
- New z = k * (1.12/0.80) * (x/y) = k * 1.4 * (x/y)
This indicates that the new z is 1.4 times the original z.
Percentage Increase in z
To find the percentage increase in z:
- Original z = k * (x/y)
- New z = 1.4 * Original z
- Percentage Increase = [(New z - Original z) / Original z] * 100
Substituting the values:
- Percentage Increase = [(1.4z - z) / z] * 100
- Percentage Increase = (0.4z / z) * 100
- Percentage Increase = 40%
Conclusion
Therefore, due to a 12% increase in x and a 20% decrease in y, there is a 40% increase in z.
When z varies directly as x and inversely as y, we can express this relationship mathematically as:
z = k * (x/y)
where k is a constant.
Initial Changes in Variables
To find the percentage change in z due to changes in x and y:
- An increase of 12% in x means:
- New x = x + 0.12x = 1.12x
- A decrease of 20% in y means:
- New y = y - 0.20y = 0.80y
Calculating the New Value of z
Substituting the new values of x and y into the equation for z:
- New z = k * (1.12x / 0.80y)
Simplifying this, we get:
- New z = k * (1.12/0.80) * (x/y) = k * 1.4 * (x/y)
This indicates that the new z is 1.4 times the original z.
Percentage Increase in z
To find the percentage increase in z:
- Original z = k * (x/y)
- New z = 1.4 * Original z
- Percentage Increase = [(New z - Original z) / Original z] * 100
Substituting the values:
- Percentage Increase = [(1.4z - z) / z] * 100
- Percentage Increase = (0.4z / z) * 100
- Percentage Increase = 40%
Conclusion
Therefore, due to a 12% increase in x and a 20% decrease in y, there is a 40% increase in z.
Community Answer
If z varies directly as x and inversely as y find the percentage incre...
40
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If z varies directly as x and inversely as y find the percentage increase in z due to an increase of 12% in x and a decrease of 20% in y ?
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If z varies directly as x and inversely as y find the percentage increase in z due to an increase of 12% in x and a decrease of 20% in y ? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about If z varies directly as x and inversely as y find the percentage increase in z due to an increase of 12% in x and a decrease of 20% in y ? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If z varies directly as x and inversely as y find the percentage increase in z due to an increase of 12% in x and a decrease of 20% in y ?.
If z varies directly as x and inversely as y find the percentage increase in z due to an increase of 12% in x and a decrease of 20% in y ? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about If z varies directly as x and inversely as y find the percentage increase in z due to an increase of 12% in x and a decrease of 20% in y ? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If z varies directly as x and inversely as y find the percentage increase in z due to an increase of 12% in x and a decrease of 20% in y ?.
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