The average daily wages of staff, consisting of supervisors and labourers, of a company is Rs. 50. The average daily wages of supervisors is Rs. 150, while that of labourers is Rs. 40 . If the number of supervisors is 15, find the number of labourers in the company.

Answer

To solve the problem step by step, let's denote:

- \( S \) = number of supervisors = 15
- \( L \) = number of labourers (which we need to find)
- \( A_s \) = average daily wages of supervisors = Rs. 150
- \( A_l \) = average daily wages of labourers = Rs. 40
- \( A \) = average daily wages of staff = Rs. 50

### Step 1: Set up the equation for average wages

The average daily wages of the entire staff can be calculated using the formula:

\[ A = \frac{(S \cdot A_s) + (L \cdot A_l)}{S + L} \]

### Step 2: Substitute the known values

Substituting the known values into the equation:

\[ 50 = \frac{(15 \cdot 150) + (L \cdot 40)}{15 + L} \]

### Step 3: Calculate the total wages of supervisors

Calculating the total wages of supervisors:

\[ 15 \cdot 150 = 2250 \]

### Step 4: Substitute the total wages back into the equation

Now substitute this back into the equation:

\[ 50 = \frac{2250 + 40L}{15 + L} \]

### Step 5: Cross-multiply to eliminate the fraction

Cross-multiplying gives us:

\[ 50(15 + L) = 2250 + 40L \]

### Step 6: Distribute on the left side

Distributing \( 50 \) on the left side:

\[ 750 + 50L = 2250 + 40L \]

### Step 7: Rearrange the equation

Now, rearranging the equation to isolate \( L \):

\[ 50L - 40L = 2250 - 750 \]

This simplifies to:

\[ 10L = 1500 \]

### Step 8: Solve for \( L \)

Dividing both sides by 10 gives:

\[ L = 150 \]

### Conclusion

The number of labourers in the company is \( L = 150 \).

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