Question

Which equation has a pair of equivalent ratios?

Answer 1

Option (3)

Explanation:

If the two ratios are equivalent then the value of the ratios will be equal.

`(x_1)/(y_1)=(x_2)/(y_2)`

Option (1)

`(11)/(12)=(44)/(46)`

Simplified form of the fraction
`(44)/(46)` is,

`(44)/(46)=(22)/(23)* (2)/(2)=(22)/(23)`

Therefore,
`(11)/(12)=(22)/(23)`

Which is not true,

Therefore, option (1) doesn't show the equivalent ratio.

Option (2)

`(36)/(40)=(4)/(9)`

Simplified form of
`(36)/(40)` is,

`(36)/(40)=(9)/(10)* (4)/(4)=(9)/(10)`

Therefore,
`(4)/(9)= (9)/(10)`

Which is not true.

Therefore, option (2) doesn't show the equivalent ratio.

Option (3)

`(1.5)/(3)=(12)/(24)`

Since simplified form of
`(1.5)/(3)` is,

`(1.5)/(3)=0.5`

And simplified form of
`(12)/(24)` is,

`(12)/(24)=0.5`

Therefore,
`(1.5)/(3)=(12)/(24)=0.5`

Option (3) shows the equivalent ratios.

Option (4)

`(8)/(12)=(4)/(24)`

Since,
`(8)/(12)=(2)/(3)* (4)/(4)=(2)/(3)`

And
`(4)/(24)=(1)/(6)* (4)/(4)=(1)/(6)`

But
`(2)/(3)\\eq (1)/(6)`

Therefore, equation in this option doesn't show the equivalent ratios.