Question : If each side of a square is decreased by 17%, then by what percentage does its area decrease?
Option 1: 25%
Option 2: 30.79%
Option 3: 31.11%
Option 4: 44.31%
Correct Answer: 31.11%
Solution :
Let the side of the square be 100.
After decrement of 17% = 83
Initial area = $(side)^2$
= $100^2$
= 10000
Area after decrement = $83^2$
= 6889
Difference in areas = 10000 – 6889 = 3111
Decrease in area (in percentage) = $\frac{\text{Decrease in area}}{\text{Initial area}}\times100$
= $\frac{3111}{10000}\times100$
= 31.11%
Hence, the correct answer is 31.11%.
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