Two numbers X and Y are respectively 20% and 28% less than a third number Z. By what percentage is the number Y less than the number X ?

The correct option is 10%.

Let us break down the solution step-by-step to understand why this is correct.

Step 1: Define the relationship of X and Y with respect to Z
Let the third number Z be represented as:
$Z=100$

Since the first number X is 20% less than Z, we can calculate its value as follows:
$X=Z-(20\%\text{of}Z)$
Substituting Z = 100:
$X=100-20=80$

Similarly, the second number Y is 28% less than Z, so we calculate its value as:
$Y=Z-(28\%\text{of}Z)$
Substituting Z = 100:
$Y=100-28=72$

Step 2: Find the difference between X and Y
Now, we find how much Y is smaller than X in terms of absolute value:
$\text{Difference}=X-Y$
$\text{Difference}=80-72=8$

Step 3: Calculate the percentage by which Y is less than X
To find by what percentage Y is less than X, we divide the difference by the value of X, and then multiply by 100:
$\text{Required Percentage}=\frac{X-Y}{X}\times 100$
Substituting the values of X and the difference:
$\text{Required Percentage}=\frac{8}{80}\times 100$
Simplifying the expression:
$\text{Required Percentage}=\frac{1}{10}\times 100=10\%$

Thus, the number Y is 10% less than the number X.