Subject: General Aptitude · Chapter: Area · Exam: 2009 · Marks: · Difficulty:
Two sides of a rectangle were measured. One of the sides (length) was measured 10\% more than its actual length and the other side (width) was measured 5\% less than its actual length. The percentage error in measure obtained for the area of the rectangle is
(a)4.5\%
(b)5\%
(c)7.56\%
(d)15\%
Answer
Answer (as printed): A
Explanation
Let the actual length and width of the rectangle be $l$ and $b$ respectively. Then, measured length $=110 \%$ of $l=\frac{11}{10} l$; measured width $=95 \%$ of $b=\frac{19}{20} b$. Actual area $=l b$. Measured area $=\left(\frac{11}{10} l \times \frac{19}{20} b\right)=\frac{209}{200} l b$. Error in measurement $=\left(\frac{209}{200} l b-l b\right)=\frac{9}{200} l b$. ∴ Error $\%=\left(\frac{9}{200} l b \times \frac{1}{l b} \times 100\right) \%=4.5 \%$.
Explanation as extracted from the printed page; notation may be imperfect.