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 $B$. 

Answer 2

Instead of introducing a multiplier variable, express each person's weight as a percentage of the total, since the ratio \( 8:7:5 \) sums to \( 20 \) parts: \( A=40\% \), \( B=35\% \), \( C=25\% \) of the total weight.

1. Option A (I alone sufficient, II not): Statement I alone gives the total, \( 300 \) kg, so \( B=35\%\times300=105 \) kg, sufficient. So this option, which denies II working, needs checking next.
2. Option B (II alone sufficient, I not): The difference \( A-C \) corresponds to \( 40\%-25\%=15\% \) of the total. Statement II gives this difference as \( 45 \) kg, so \( 15\% \) of the total \( =45\Rightarrow \) total \( =300 \) kg, and hence \( B=35\%\times300=105 \) kg, also sufficient. So this option, which denies I working, is also not the full picture.
3. Option C (either alone sufficient): As shown, both I alone and II alone independently pin down the total weight, and hence \( B \), via the percentage breakdown. This matches.
4. Option D (even together not sufficient): Since even one statement alone already suffices, this option is clearly false.
5. Option E (I + II together necessary): This is unnecessary, since either statement alone already determines \( B \); rejected.

Both statements independently fix the total weight via the percentage shares, so either one alone answers the question.

Hence, the correct answer is If either I alone or II alone is sufficient.