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

1. Statement I: Total weight \( 300 \) kg divided in ratio \( 8:7:5 \) (\( 20 \) parts) gives one part \( =15 \) kg, so \( B=7\times15=105 \) kg, sufficient alone.
2. Statement II: The difference \( A-C \) corresponds to \( 8-5=3 \) parts \( =45 \) kg, so one part \( =15 \) kg, giving \( B=7\times15=105 \) kg, also sufficient alone.

Both statements independently yield \( B=105 \) kg, so either one alone is enough to answer the question.