Question

A carpenter cuts off from a plank of wood 7/3 of its length and then 2/3 of what remains. If the  remaining piece is  4 whole 1/2 m long, find the original length of the plank.​

Answer 1

Answer:

Let the Original length of the Plank be x m.

∴ Part of the Plank cut = 5/12 x x

= 5x/12 m.

Now, Remaining part of the plank = x - 5x/12

= (12x - 5x)/12

= 7x/12 m

A/c to the Question,

Carpenter cuts 6/7th part of the 7x/12 m.

∴ Length of the Part cut = 7x/12 x 6/7

= x/2 m.

Now, Remaining Part = 5/2 m.

We know,

∴ 5x/12 + x/2 + 5/2 = x

⇒ (5x + 6x + 30)/12 = x

⇒ 11x + 30 = 12x

⇒ 12x - 11x = 30

∴ x = 30 m.

Hence, the length of the Plank is 30 m.