Question

A, B, C and D purchased a restaurant for Rs. 56 lakhs. The contribution of B, C and D together is 460% that of A alone. The contribution of A, C and D together is \(366\dfrac{2}{3}\%\) that of B's contribution, and the contribution of C is 40% that of A, B and D together. The amount contributed by D is:

• A. 10 lakhs
• B. 12 lakhs
• C. 16 lakhs
• D. 18 lakhs

Hint:

Each clue is really “total minus one person”; rewrite each as (56 - X) = ratio × X and solve for A, B, C directly, then D by subtraction.

Answer 1

The Correct Option is D

Step 1: Set up the total.
\(A+B+C+D=56\) (Eq 1).

Step 2: Translate each condition into an equation.
\(B+C+D=4.6A\) (Eq 2). \(A+C+D=\dfrac{11}{3}B\) (Eq 3, since \(366\tfrac{2}{3}\%=\dfrac{1100}{3}\%=\dfrac{11}{3}\) as a multiplier). \(C=0.4(A+B+D)\), i.e. \(A+B+D=2.5C\) (Eq 4).

Step 3: Solve for A using Eq 1 and Eq 2.
From Eq 2, \(56-A=4.6A \Rightarrow 56=5.6A \Rightarrow A=10\).

Step 4: Solve for B using Eq 1 and Eq 3.
From Eq 3, \(56-B=\dfrac{11}{3}B \Rightarrow 56=B\left(1+\dfrac{11}{3}\right)=B\times\dfrac{14}{3} \Rightarrow B=56\times\dfrac{3}{14}=12\).

Step 5: Solve for C using Eq 1 and Eq 4.
From Eq 4, \(56-C=2.5C \Rightarrow 56=3.5C \Rightarrow C=16\).

Step 6: Solve for D.
\(D=56-A-B-C=56-10-12-16=18\).

Step 7: Final Answer.
D contributed 18 lakhs, so option D is correct.