Question

A naughty student breaks the pencil in such a way that the ratio of two broken parts is same as that

of the original length of the pencil to one of the larger part of the pencil. The ratio of the other part

to the original length of pencil is

Answer 1

so let the length of the larger part be x and of smaller part be y
so there ratio is x is to y=K X + k y/kx
x/y=x+y/x
so x²/(x+y)²=y/x+y
or the ratio of smaller part to the length of whole pencil is equal to square of the ratio of larger part by the square of length of hold pencil

Answer 2

Answer:

Let the pencil be broken in ratio 1:k where k being a greater fraction.

According to the condition:

1/k=k/(k+1)

k^2 - k - 1 =0

k=(1+√5) /2