QUESTION

CSAT

Medium

Maths

Prelims 2016

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 numbers X?

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Explanation

Let the third number be Z.

X is 20% less than Z: $X = Z \cdot (1 - 20\%) = Z \cdot 0.80$ Y is 28% less than Z: $Y = Z \cdot (1 - 28\%) = Z \cdot 0.72$ To find the percentage by which Y is less than X, use the formula: Percentage decrease = $((X - Y) / X) \cdot 100$

Substituting values of X and Y: Percentage decrease = $((0.80 \cdot Z - 0.72 \cdot Z) / (0.80 \cdot Z)) \cdot 100$ Percentage decrease = $((0.08 \cdot Z) / (0.80 \cdot Z)) \cdot 100$ Percentage decrease = $0.10 \cdot 100$ Percentage decrease = 10%