A man, a woman and a girl worked for a contractor for the same 'period. A man is twice efficient as a woman and a woman is thrice efficient as a girl ₹10000 were given to all of them. What is the sum of money received by a woman and a girl together?

Options

A. ₹ 5500
B. ₹ 4500
C. ₹ 4000
D. ₹ 6000

Answer

To solve the problem step by step, let's break it down:

1. **Understanding the Efficiency Ratios**:
- Let the efficiency of the girl be \( G \).
- According to the problem, the woman is thrice as efficient as the girl, so the efficiency of the woman \( W = 3G \).
- The man is twice as efficient as the woman, so the efficiency of the man \( M = 2W = 2(3G) = 6G \).

2. **Establishing the Efficiency Ratio**:
- Now we have the efficiencies:
- Man: \( 6G \)
- Woman: \( 3G \)
- Girl: \( G \)
- The ratio of their efficiencies can be expressed as:
\[ M : W : G = 6G : 3G : G = 6 : 3 : 1 \]

3. **Calculating Total Efficiency**:
- The total efficiency is the sum of their efficiencies:
\[ 6 + 3 + 1 = 10 \]

4. **Distributing the Total Payment**:
- The total payment is ₹10,000.
- The payment for each unit of efficiency is:
\[ \text{Value of one unit} = \frac{10000}{10} = 1000 \text{ rupees} \]

5. **Calculating the Payment for the Woman and Girl**:
- The woman has an efficiency of \( 3G \) which corresponds to \( 3 \) units.
- The girl has an efficiency of \( G \) which corresponds to \( 1 \) unit.
- Together, the woman and girl have:
\[ 3 + 1 = 4 \text{ units} \]
- The total amount received by the woman and girl together is:
\[ \text{Amount} = 4 \text{ units} \times 1000 \text{ rupees/unit} = 4000 \text{ rupees} \]

6. **Final Answer**:
- Therefore, the sum of money received by the woman and the girl together is ₹4,000.