Question

The length of rope A is $1\frac{3}{5}$ meters and the length of rope B is $\frac{1}{2}$ times the length of rope A. Which of the following statements is correct?
Statement 1: The length of rope A is less than the length of rope B.
Statement 2: The length of rope B is $\frac{2}{5}$ meters.

• A. Only statement $1$ is correct.
• B. Both statements are correct.
• C. Both statements are incorrect.
• D. Only statement $2$ is correct.

Answer 1

The correct option is C Both statements are incorrect.

$LengthofropeA=1\frac{3}{5}m$
$LengthofropeB=\frac{1}{2}\times thelengthofropeA$
$=\frac{1}{2}\times 1\frac{3}{5}m$
Here, $\frac{1}{2}<1$
When a given number is multiplied by a fraction less than one, the product will be less than the given number.
$1\frac{3}{5}=\frac{8}{5}$
$1\frac{3}{5}\times \frac{1}{2}=\frac{8}{5}\times \frac{1}{2}=\frac{8}{10}=\frac{8÷2}{10÷2}=\frac{4}{5}m$
So, the product of $1\frac{3}{5}$ and $\frac{1}{2}$ is less than $1\frac{3}{5}$.
And the length of rope B is $\frac{4}{5}m.$
Thus, both the statements are incorrect.