1/8 part of a pencil is black and 1/2 part of the remaining is white. If the remaining part is blue and length of this blue part is 31/2 cm, then find the length of the pencil.

Let total length of pencil be x cm.
Then, black part = x/8
Remaining part pencil after black part = x - x/8 = 7x/8
then White part = 1/2 (7x/8)
= 7x/16
Now Remaining part of pencil is blue = total length of pencil - (length of black part + length of white part)
length of blue part of pencil = x - (x/8 + 7x/16)
length of blue part of pencil = x - (2x + 7x)/16
length of blue part of pencil = x - 9x/16
length of blue part of pencil = (16 x - 9x)/16
∴ Length of blue part = 7x/16;
According to question
Length of blue part = 3¹/₂
7x/16 = 3¹/₂
⇒ 7x/16 = 7/2
⇒ x/16 = 1/2
⇒ x = 16/2
∴ x = 8 cm