Q. 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? (UPSC Prelims 2010)
Answer: 10%
Notes: Assume Z = 100. Then X = 80 (20% less than 100) and Y = 72 (28% less than 100). The difference between X and Y is 8. The percentage by which Y is less than X is calculated as (8/80) × 100% = 10%. Alternatively, using X = 0.8Z and Y = 0.72Z, (X - Y)/X = 0.1, confirming Y is 10% less than X. This standard percentage decrease calculation compares the difference relative to X’s value.