If one-eighth of a pencil is black, half of the remaining is white and the remaining 3 cm is blue, find the total length
of the pencil.

One-eighth of a pencil is black

Half of the remaining is white

Remaining 3 cm is blue.

Total length of the pencil = x cm

​$$\frac {1} {8} \times x$$ = Black

Remaining :- $$x-\frac {x} {8} = \frac {7x} {8}$$

White = $$\frac{1}{2} \left( \frac{7x}{8} \right)$$=$$\frac {7x}{16}$$ cm

x-$$\frac {7x}{16}$$ = 3

​$$\frac {7x}{8} - \frac {7x} {16}$$= 3

$$\frac{7x}{8} \left( 1 - \frac{1}{2} \right)$$=$$3$$

$$\frac {7x} {16}=3$$​​​

​​

​$$7x= 16 \times 3$$ 

​$$x= \frac {48}{7} = 6.8$$

Thus, the correct answer is (D) 6.5 cm