15 men, 18 women and 12 boys working together earned ₹ 2070. If the daily wages of a man, a woman and a boy are in the ratio of 4 : 3 : 2, the daily wages (in ₹) of 1 man, 2 women and 3 boys are

### Concept & Total Wage Calculation The total earnings of a mixed group of workers are found by summing the products of the number of workers in each category and their respective individual daily wages. $$\text{Total Earnings} = \sum (\text{Number of Workers} \times \text{Individual Wage})$$ ### Step-by-Step Solution 1. **Define Individual Wages:** Given the ratio $4 : 3 : 2$, let the daily wages of 1 man, 1 woman, and 1 boy be $4x$, $3x$, and $2x$ respectively. 2. **Calculate Total Earnings Equation:** Total earnings = $(15 \times 4x) + (18 \times 3x) + (12 \times 2x)$ Total earnings = $60x + 54x + 24x = 138x$ 3. **Solve for Multiplier ($x$):** We are given that the total actual earnings are ₹ 2070. $138x = 2070$ $x = \frac{2070}{138} = 15$ 4. **Formulate Target Equation:** We need to find the total combined daily wage for 1 man, 2 women, and 3 boys. Target wage = $1(4x) + 2(3x) + 3(2x)$ Target wage = $4x + 6x + 6x = 16x$ 5. **Final Calculation:** Substitute $x = 15$ into the target wage equation. Target wage = $16 \times 15 = 240$ ### Exam Strategy & Shortcut Instead of calculating the absolute individual wages for a man (₹ 60), woman (₹ 45), and boy (₹ 30) and then summing them up for the required group, keep everything in terms of the ratio multiplier '$x$'. Calculate the final required value as $16x$ and substitute $x = 15$ at the very end to minimize arithmetic operations and save time. ### Common Pitfall A common mistake is correctly finding the individual wages ($60$, $45$, $30$) but then forgetting to multiply them by the required number of people ($1, 2, 3$) in the final step, mistakenly choosing $60 + 45 + 30 = 135$ (Option a). ### Final Answer Therefore, the correct answer is **240**.