Question

The ratio x: y is 1:3

Which of the following statements are correct?
A x is 1/3 of y
B y is 3/4 of (x + y)
x is 1/4 of y
y is 3/4 of x

Answer 1

A and B

x is
`(1)/(3)` of y

AND

y is
`(3)/(4)` of (x+y)

Explanation:

x:y is 1:3

=> y is bigger than x

=> y is 3x bigger than x

=> y = 3 lots of x

=>
`y =`
`3x`

=>
`(y)/(3)`
`= x`

=>
`(1)/(3) y`
`= x`

So x is
`(1)/(3)` of y

y is
`(3)/(4)` of (x+y)

If x = 1 and y = 3 (substitute in values)

=> 3 is
`(3)/(4)` of (4)

=> 3 is
`(3)/(4)`(4)

=> 3 is (
`(3)/(4)`x4)

=> 3 = 3

Therefore, y is
`(3)/(4)` of (x+y) is true

So the answers are:

x is
`(1)/(3)` of y

AND

y is
`(3)/(4)` of (x+y)

Answer 2

Option A

Explanation:

x : y = 1 : 3

This can be also written as

`(x)/(y) = (1)/(3)`

Multiplying y on both the sides

`= > (x)/(y) * y = (1)/(3) * y`

`= > x = (1)/(3) * y`

Hence , x is one-third of y