Question

The length of a wire is decreased by $12\frac{1}{2}\%$. What is the new length if it was $150metres$ ?

Answer 1

Step 1: Finding the decrease in length equivalent to $12\frac{1}{2}\%$.

Original length of wire $=150m$

Converting mixed fraction into improper fraction $12\frac{1}{2}\%=\frac{\left(12\times 2\right)+1}{2}=\frac{25}{2}\%$

Therefore, decrease in value will be,

$$\begin{gathered} \Rightarrow 12\frac{1}{2}\%of150m=\frac{25}{2}\%\times 150 \\ \Rightarrow \frac{25}{2\times 100}\times 150=\frac{25\times \cancel{150}3}{2\times \cancel{100}2}=\frac{75}{4} \\ \Rightarrow \frac{75}{4}=18.75m \end{gathered}$$

Hence, the wire is to be decreased by $18.75m$

Step 2: Finding the new length.

$\Rightarrow$Original length $-$ Value to be decreased

$\Rightarrow 150m-18.75m=131.25m$

Hence, the new length of wire is $131.25m$.