Question

The weights of $A$, $B$ and $C$ are in the ratio $8:7:5$. $A$'s weight is $60\%$ more than $C$'s. Find the weight of $B$.
I. Total weight of $A,B,C$ is $300$ kg.
II. Difference between $A$'s and $C$'s weight is $45$ kg. 

• A. I alone sufficient; II alone not.
• B. II alone sufficient; I alone not.
• C. Either I alone or II alone sufficient.
• D. Even I + II together not sufficient.
• E. I + II together necessary.

Hint:

When a ratio is given, any one linear anchor (total or a difference) fixes the scale factor and hence all individual values.

Answer 1

The Correct Option is C

Let $A: B: C = 8:7:5$ (consistent with $A=1.6C$).
I: $8k+7k+5k=300 \Rightarrow k=15 \Rightarrow B=7k=105$ kg (sufficient).
II: $A-C=45$ and with $A=8k,\,C=5k$ gives $3k=45\Rightarrow k=15 \Rightarrow B=105$ kg (sufficient).
Either statement gives $B$.