Answer:
Statement (2) is sufficient.
Step-by-step explanation:
Here, m, r, x and y are positive numbers,
We have to check :
[tex]\frac{m}{r}=\frac{x}{y}[/tex]
Statement (1) :
The ratio of m to y is equal to the ratio of x to r,
i.e.
[tex]\frac{m}{y}=\frac{x}{r}[/tex]
[tex]mr = xy[/tex] ( By cross multiplication )
Thus, statement (1) is not sufficient.
Statement (2) :
The ratio of m + x to r + y is equal to the ratio of x to y
[tex]\frac{m+x}{r+y}=\frac{x}{y}[/tex]
By cross multiplication,
y(m+x) = x(r+y)
By distributive property,
ym + yx = xr + xy
Using subtracting property of equality,
ym = xr
[tex]\frac{m}{r}=\frac{x}{y}[/tex]
Hence, proved...
i.e. statement (2) is sufficient.
