Question

Divide a rope of length 560 cm into 2 parts such that twice the length of the smaller part is equal to $\frac{1}{3}$ of the larger part. Then find the length of the larger part.

Answer 1

Let the smaller part be x cm and larger part be y cm.
$x+y=560$ .....(I)
Twice the length of the smaller part is equal to $\frac{1}{3}$ of the larger part.
$$\begin{gathered} x=\frac{1}{3}y \\ \Rightarrow 3x=y \end{gathered}$$
Putting the value of y in (I) we have
$$\begin{gathered} x+3x=560 \\ \Rightarrow 4x=560 \\ \Rightarrow x=140 \end{gathered}$$
And thus, $y=3\times 140=420$
Thus, the larger part = 420 cm and smaller part is 140 cm.