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An empty metal container (without its handle) weight 15% of its weight when filled with a particular liquid. after adding the handle, the weight of the fully filled container increases by 5%. if the weight of a partly filled container is 1/3 of the completely filled container with handle attached, then what fraction of container is utilized
(A) 317
(B) 417
(C) 619
(D) 319

Answer
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Hint:In this question the total weight of container without handle is not given so by assuming it as 100g we can find weight of liquid and weight of container. In this we convert percentage in fraction by using x%=x100 .

Complete step-by-step answer:
Now we assume that a full container without the handle weighed 100g to find the weight fraction.
So total weight of container without handle is 100g
Now according to the question the weight of an empty container is 15% of the total weight of the container.
Weight of empty container =15×100100
So weight of empty container is 15g
Now we have to find weight of liquid filled in container
Weight of liquid = total weight of container – weight of empty container
Weight of liquid =100g15g
Weight of liquid = 85g
Now, adding a handle adds 5% or 5 grams,
So a full container with a handle would weight = 100g+5g
Full weight of container with handle = 105g
 Given, the weight of a partly filled container is 1/3 of the completely filled container with handle
So weight of partly filled container = 13×105g
Weight of partly filled container = 35g
Now to find fraction of container utilize is find by subtracting the weights of container and the handle
 So 35g5g15g=15g
Now calculating our fraction we have,
Ratio of liquid present in partly filled container and fully filled container
 So 15g85g
fraction of container utilize = 317
So option A is the correct answer.

Note:we can do this question by assuming the weight of container as variable X.
So total weight of container without handle=x
Weight of container= 15%of x
15×x100
.15x
Now weight of liquid filled in container
x.15x=.85x
Now weight of container with handle is x+5%of x
x+0.05x
1.05x
the weight of a partly filled container is 1/3 of the completely filled container with handle
So weight of partly filled container=13×1.05x
.35x
Now fraction of container utilize is find by subtracting the weights of container and the handle
.35x.05x.15x
.15x
Now fraction of container =.15x.85x
So fraction of container = 317