Question

Divide a rope of length 560 cm into 2 parts such that twice the length of the smaller part is equal to ⅓ of the larger. Then find the length of the larger part.​

Answer 1

Answer:

The length of the larger part of the rope is 480 cm.

Step-by-step-explanation:

Let the length of the larger part of the rope be x cm.

And the length of the smaller part of the rope be y cm.

From the first condition,

The length of the rope is 560 cm.

∴ x + y = 560

⇒ y = 560 - x

⇒ y = - x + 560 - - - ( 1 )

From the second condition,

Twice the length of the smaller part is equal to the one-third of the larger part of the rope.

$\displaystyle{\therefore\:\sf\:2y\:=\:\dfrac{1}{3}\:\times\:x}$

$\displaystyle{\implies\sf\:2\:\times\:(\:-\:x\:+\:560\:)\:=\:\dfrac{x}{3}\:\quad\:-\:-\:-\:[\:From\:(\:1\:)\:]}$

$\displaystyle{\implies\sf\:-\:2x\:+\:1120\:=\:\dfrac{x}{3}}$

$\displaystyle{\implies\sf\:3\:\times\:(\:-\:2x\:+\:1120\:)\:=\:x}$

$\displaystyle{\implies\sf\:x\:=\:-\:6x\:+\:3360}$

$\displaystyle{\implies\sf\:x\:+\:6x\:=\:3360}$

$\displaystyle{\implies\sf\:7x\:=\:3360}$

$\displaystyle{\implies\sf\:x\:=\:\cancel{\dfrac{3360}{7}}}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:x\:=\:480\:cm}}}}$

∴ The length of the larger part of the rope is 480 cm.

Answer 2

see the attachment....