Question

Divide a rope of length $560cm$ 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 $=x$

then the second part $=560-x$

Now, according to the question

$2x=\frac{1}{3}(560-x)$

$\Rightarrow 2x=\frac{560}{3}-\frac{x}{3}$

$\Rightarrow 6x=560-x$

$\Rightarrow 6x+x=560$

$\Rightarrow 7x=560$

$\therefore x=80$

so, smaller part $=80$cm

larger part $=(560-80)=480$cm