Question

One cut of a rope produces two pieces. Two cut produces three pieces. Three cuts produces four pieces . How many pieces are produced by 8 cuts?

Answer 1

We observe here that $1$ cut produces $2$ pieces,$2$ cut produces $3$ pieces

Thus when it is $n$ cuts there will be $n+1$ pieces

Given:

$1$ cut produces $2$ pieces,$2$ cut produces $3$ pieces
$3$ cut produces $4$ pieces

When it is $n$ cuts there will be $n+1$ pieces

Thus, $8$ cut produces $8+1=9$ pieces

Answer 2

9 pieces of a rope will be produced by 8 cuts.

• It is given that one cut produces two pieces of a rope, and two cuts produce three pieces. Similarly, three cuts produce four pieces, and so on.
• Thus, it can be observed that if 'n' cuts are made, the number of pieces of the rope produced is one more than the number of cuts, that is, the number of pieces = 'n + 1'.
• So, if we put n = 8, that is 8 cuts, we get the number of pieces produced as n + 1 = 8 + 1 = 9.
• Therefore, 9 pieces are produced by 8 cuts.