In a farm equipment manufacturing firm, the ratio of skilled technicians to engineers is 5:3. If 20 additional engineers are hired, the new ratio becomes 5:4. The total initial number of technicians and engineers in the firm was ________ (in integer).
Answer Key:
160
Step-by-Step Solution & Explanation
1. Let initial number of technicians be $5x$ and engineers be $3x$.
2. After adding 20 engineers:
$\frac{5x}{3x + 20} = \frac{5}{4}$
3. Cross-multiplying:
$4(5x) = 5(3x + 20)$
$20x = 15x + 100$
$5x = 100 \implies x = 20$
4. Initial technicians = $5 \times 20 = 100$.
5. Initial engineers = $3 \times 20 = 60$.
6. Total initial workforce = $100 + 60 = 160$.