Class 6 Exam > Class 6 Questions > If x : y : : y : z, identify the correct stat...
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If x : y : : y : z, identify the correct statement from among the following.
- a)xy = yz
- b)y2 = xz
- c)xyz = x
- d)zy = x
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If x : y : : y : z, identify the correct statement from among the foll...
x:y::y:z
x/y=y/z now cross multiply
y2=xz
⇒y2=xz
x/y=y/z now cross multiply
y2=xz
⇒y2=xz
Most Upvoted Answer
If x : y : : y : z, identify the correct statement from among the foll...
Given Information:
The given ratio is x : y :: y : z.
To find:
The correct statement from the given options.
Solution:
The given ratio is x : y :: y : z.
This means that the ratio of x to y is equal to the ratio of y to z.
We can write this as:
x/y = y/z
Now, let's analyze the given options:
a) xy = yz
This option is not correct because the product of x and y is not equal to the product of y and z. The given ratio does not imply that the products are equal.
b) y^2 = xz
This option is correct. By rearranging the equation x/y = y/z, we get y^2 = xz. This shows that the square of y is equal to the product of x and z.
c) xyz = x
This option is not correct. The given ratio does not imply that the product of x, y, and z is equal to x.
d) zy = x
This option is not correct. The given ratio does not imply that the product of z and y is equal to x.
Conclusion:
The correct statement from the given options is option 'B': y^2 = xz.
The given ratio is x : y :: y : z.
To find:
The correct statement from the given options.
Solution:
The given ratio is x : y :: y : z.
This means that the ratio of x to y is equal to the ratio of y to z.
We can write this as:
x/y = y/z
Now, let's analyze the given options:
a) xy = yz
This option is not correct because the product of x and y is not equal to the product of y and z. The given ratio does not imply that the products are equal.
b) y^2 = xz
This option is correct. By rearranging the equation x/y = y/z, we get y^2 = xz. This shows that the square of y is equal to the product of x and z.
c) xyz = x
This option is not correct. The given ratio does not imply that the product of x, y, and z is equal to x.
d) zy = x
This option is not correct. The given ratio does not imply that the product of z and y is equal to x.
Conclusion:
The correct statement from the given options is option 'B': y^2 = xz.
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If x : y : : y : z, identify the correct statement from among the following.a)xy=yzb)y2=xzc)xyz=xd)zy=xCorrect answer is option 'B'. Can you explain this answer?
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