A man and a boy received Rs.1400 as wages for 10 days for the work they did together. The man's effi-ciency in the work was six times that of the boy. What is the daily wages of the boy?

Options

A. no
B. RS. 15
C. Rs.20
D. Rs. 30

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Understand the problem
We have a man and a boy who worked together for 10 days and earned a total of Rs. 1400. The efficiency of the man is 6 times that of the boy.

### Step 2: Define efficiencies
Let the efficiency of the boy be \( E_b = 1 \). Then, the efficiency of the man will be \( E_m = 6 \) (since the man's efficiency is six times that of the boy).

### Step 3: Calculate total efficiency
The total efficiency of both the man and the boy combined is:
\[ E_{total} = E_b + E_m = 1 + 6 = 7 \]

### Step 4: Calculate the share of wages
The total wages for 10 days is Rs. 1400. We need to find the share of the boy in these wages. The share of the boy can be calculated as follows:
\[ \text{Boy's share} = \frac{E_b}{E_{total}} \times \text{Total Wages} \]
Substituting the values:
\[ \text{Boy's share} = \frac{1}{7} \times 1400 = 200 \]

### Step 5: Calculate daily wages of the boy
Now that we have the boy's total share of Rs. 200 for 10 days, we can find his daily wages:
\[ \text{Daily wages of the boy} = \frac{\text{Boy's share}}{\text{Number of days}} = \frac{200}{10} = 20 \]

### Conclusion
The daily wages of the boy is Rs. 20.

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