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

Each of the three percentage clues actually describes “the total minus one person”, which makes it easy to isolate that one person directly using the grand total of 56.

1. “B+C+D is 460% of A” really means (56 - A) = 4.6A, since B+C+D = 56 - A. Solving: $56 = 5.6A \Rightarrow A = 10$.
2. “A+C+D is 366⅔% of B” means (56 - B) = $\frac{11}{3}$B. Solving: $56 = \frac{14}{3}B \Rightarrow B = 12$.
3. “C is 40% of A+B+D” means C = 0.4(56 - C), so $C = 22.4 - 0.4C \Rightarrow 1.4C = 22.4 \Rightarrow C = 16$.
4. With A, B, C known, D follows directly: $D = 56 - 10 - 12 - 16 = 18$.

So the correct answer is option D, 18 lakhs.