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?

Correct Option (B)

To determine the percentage by which number Y is less than number X, we first establish the values of X and Y relative to a third number Z.

• Assume the third number Z = 100.
• Number X is 20% less than Z:

X = \(100 - \frac{20}{100} \times 100 = 80\)

• Number Y is 28% less than Z:

Y = \(100 - \frac{28}{100} \times 100 = 72\)

• The absolute difference between X and Y is:

Difference = \(80 - 72 = 8\)

• To calculate the percentage by which Y is less than X, the difference is expressed as a percentage of X:

Required percentage = \(\frac{8}{80} \times 100 = 10\%\)

Incorrect Options:

Options A (12%), C (9%), and D (8%) are incorrect. These values do not represent the accurate percentage by which Y is less than X. Option D (8%) represents the absolute difference between X and Y, not the percentage difference relative to X. The other incorrect options likely result from miscalculations or using an incorrect base for the percentage computation.