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 366.66% 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

Answer 1

The Correct Option is D

To solve this problem, let's denote the contributions of A, B, C, and D as \( a \), \( b \), \( c \), and \( d \) respectively, in lakhs. We have the following pieces of information:

1. The total purchase price of the restaurant is \( a + b + c + d = 56 \) lakhs.
2. The contribution of B, C, and D together is 460% of A's contribution: \[ b + c + d = 4.6a \]
3. The contribution of A, C, and D together is 366.66% of B's contribution: \[ a + c + d = \frac{366.66}{100}b = 3.6666b \]
4. The contribution of C is 40% of the total contribution of A, B, and D: \[ c = 0.4(a + b + d) \]

We now have four equations to solve:

1. \( a + b + c + d = 56 \)
2. \( b + c + d = 4.6a \)
3. \( a + c + d = 3.6666b \)
4. \( c = 0.4(a + b + d) \)

Let's solve these equations step by step. From the second equation, express \( d \) in terms of \( a \):

\( d = 4.6a - b - c \)

From the third equation, express \( a \) in terms of \( b \):

\( a = 3.6666b - c - d \)

Using the fourth equation, substitute \( c \):

\( c = 0.4(a + b + d) \)

Substituting the expression for \( d \) from equation 2 into the other equations, the solutions simplify to find the values of \( a \), \( b \), \( c \), and \( d \). Solving these will give:

\( b = 15 \), \( c = 9 \), \( d = 18 \)

Therefore, the amount contributed by D is \( 18 \) lakhs.