Word Problem

[Abdulla]

Any empty metal box weighs 10 percent of its total weight when filled with varnish. If the weight of a partly filled box is one-half that of a completely filled box, what fraction of the box is filled ?

(A) 3/5
(B) 5/9
(C) 1/2
(D) 4/9
(E) 2/5

OA is D

[anayeri]

Let's plug in some numbers (easy ones!).

let's say a filled box weighs 10lbs total. So 10% of that weight is the empty box (0.1*10lbs=1lb).

So if a partly filled box weighs half of a totally filled box (10lbs):

Totally Fill:
1lb (empty) + 9lbs fill =10lbs

Partly Fill:
1lb (empty) + xlbs = 5lbs (half of 10).

So x = 4.

How much of the box is full?

4lbs out of a possible 9lbs is full.

4/9, hence D.