Question

A carpenter cuts off from a plank 5/12 of its length and then 6/7 of what remains. If the remaining piece is 2 and 1/2 m long, find the original length of the plank.

Answer 1

Let the Original length of the Plank be x m.

∴ Part of the Plank cut = 5/12 × 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 × 6/7
= x/2 m.

Now, Remaining Part = 2.5 = 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.