One-fourth part of a pencil is black, half of the remaining part is green and the rest of the pencil is yellow. If the length of the yellow part is $$1\frac{1}{2}$$​ cm, then find the length of the pencil.

Correct option is D

Given:
One-fourth of the pencil is black.
Half of the remaining part is green.
The rest is yellow, with a length of $$1 \frac{1}{2}$$​ cm (which is 1.5 cm).
Solution:

Let the total length of the pencil be L cm.

Black =$$\frac{1}{4}L$$​
Remaining Length:
L -$$\frac{1}{4}L = \frac{3}{4}L$$​
Green = $$\frac{1}{2} \times \frac{3}{4}L = \frac{3}{8}L$$​
Remaining Length (Yellow):
$$\frac{3}{4}L - \frac{3}{8}L = \frac{6}{8}L - \frac{3}{8}L = \frac{3}{8}L$$​​

Given that the Yellow Part is 1.5 cm:
$$\frac{3}{8}L = 1.5 \text{ cm}$$​​
L $$= 1.5 \times \frac{8}{3} = 4 \text{ cm}$$​