If 7 : 21 :: 2.2 : x and 7 : 49 :: 9 : y, what is the ratio of x to y?

The correct answer is Option 11 : 105.

Step 1: Find the value of x

We are given the proportion:

$7:21::2.2:x$

Writing this as an equation in fractional form:

$\frac{7}{21}=\frac{2.2}{x}$

Simplifying the fraction on the left side:

$\frac{1}{3}=\frac{2.2}{x}$

Cross-multiplying gives:

$x=2.2\times 3=6.6$

Step 2: Find the value of y

We are given the proportion:

$7:49::9:y$

Writing this as an equation in fractional form:

$\frac{7}{49}=\frac{9}{y}$

Simplifying the fraction on the left side:

$\frac{1}{7}=\frac{9}{y}$

Cross-multiplying gives:

$y=9\times 7=63$

Step 3: Calculate the ratio of x to y

Now, substitute the values of x and y into the ratio:

$\frac{x}{y}=\frac{6.6}{63}$

Multiply both numerator and denominator by 10 to clear the decimal:

$\frac{x}{y}=\frac{66}{630}$

Divide both the numerator and the denominator by their greatest common divisor, 6:

$\frac{x}{y}=\frac{66÷6}{630÷6}=\frac{11}{105}$

Therefore, the ratio of x to y is 11 : 105.