Question

A sum of 6,765 is divided among Ram, Lakshman and Kishan in such a way that when 29, 46 and 30 is deducted from their respective shares, the ratio of money with them becomes 49 : 34 : 65. What is the share of B?

• A. 1,576
• B. 1,476
• C. 1,376
• D. 1,676

Answer 1

The Correct Option is A

Finding the Share of Lakshman 

Given Conditions:

• Total sum: \[ R + L + K = 6765 \]
• After deducting specific amounts, the new ratio is: \[ \frac{R - 29}{49} = \frac{L - 46}{34} = \frac{K - 30}{65} \]

Step 1: Expressing \( R, L, K \) in Terms of \( x \)

Let the common ratio be \( x \), then:

\[ R = 49x + 29 \]

\[ L = 34x + 46 \]

\[ K = 65x + 30 \]

Step 2: Substituting in the Total Sum Equation

Substituting \( R, L, \) and \( K \) into the equation:

\[ (49x + 29) + (34x + 46) + (65x + 30) = 6765 \]

Step 3: Solving for \( x \)

Combining like terms:

\[ 148x + 105 = 6765 \]

Subtracting 105 from both sides:

\[ 148x = 6660 \]

Dividing by 148:

\[ x = \frac{6660}{148} = 45 \]

Step 4: Finding Lakshman’s Share

Using the formula for \( L \):

\[ L = 34x + 46 = 34 \times 45 + 46 \]

\[ L = 1530 + 46 = 1576 \]

Final Answer:

Thus, the share of Lakshman is 1,576. The correct option is (A).