A 70 cm long wire is to be cut into two pieces such that one piece will be $\frac{2}{5}$ as long as the other. How many centimetres will the shorter piece be?
(a)10
(b)14
(c)20
(d)28
Answer
Answer (as printed): C
Explanation
Let the length of longer piece be $x \mathrm{cm}$. Then, length of shorter piece $=\left(\frac{2}{5} x\right) \mathrm{cm}$. $$\therefore \quad x+\frac{2}{5} x=70 \Leftrightarrow \frac{7 x}{5}=70 \Leftrightarrow x=\left(\frac{70 \times 5}{7}\right)=50 .$$ Hence, length of shorter piece $=\frac{2}{5} x=\left(\frac{2}{5} \times 50\right) \mathrm{cm}=20 \mathrm{cm}$.