A man has 3 sons, 2 daughters and a wife. They divided a sum ofRs. 19000 among themselves such that each daughter got 1.5 times the amount received by each son and his wife received Rs. 600 less than each son. What is the total amount (in Rs.) received by the three sons together?

Options

A. 2800
B. 3600
C. 5600
D. 8400

Answer

To solve the problem, let's denote the amount received by each son as \( S \).

1. **Identify the amounts received by each family member:**
- Amount received by each son = \( S \)
- Amount received by each daughter = \( 1.5S \)
- Amount received by the wife = \( S - 600 \)

2. **Calculate the total amount received by all family members:**
- There are 3 sons, 2 daughters, and 1 wife.
- Total amount received by the sons = \( 3S \)
- Total amount received by the daughters = \( 2 \times 1.5S = 3S \)
- Amount received by the wife = \( S - 600 \)

3. **Set up the equation for the total amount:**
- The total amount distributed among them is Rs. 19000.
- Therefore, we can write the equation:
\[ 3S + 3S + (S - 600) = 19000 \]

4. **Combine like terms:**
- Simplifying the equation gives:
\[ 7S - 600 = 19000 \]

5. **Solve for \( S \):**
- Adding 600 to both sides:
\[ 7S = 19000 + 600 \]
\[ 7S = 19600 \]
- Now, divide both sides by 7:
\[ S = \frac{19600}{7} = 2800 \]

6. **Calculate the total amount received by the three sons:**
- Total amount received by the three sons = \( 3S = 3 \times 2800 = 8400 \)

Thus, the total amount received by the three sons together is **Rs. 8400**.