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Linear Equations
A factory manufactures two types of industrial valves, Type $A$ and Type $B$. The profit earned on each Type $A$ valve is ₹120, while the profit earned on each Type $B$ valve is ₹200. On a particular day, the total profit earned from the sale of these valves was ₹6,480. If the number of Type $B$ valves sold was $4$ less than twice the number of Type $A$ valves sold, determine the number of Type $A$ valves sold. A) $10$ B) $12$ C) $14$ D) $16$
Correct Answer: **C) 14** Let the number of Type $A$ valves sold be $x$. According to the question, the number of Type $B$ valves sold is: $$2x - 4$$ Profit from Type $A$ valves: $$120x$$ Profit from Type $B$ valves: $$200(2x - 4)$$ Total profit is ₹6,480. Therefore, $$120x + 200(2x - 4) = 6480$$ Now solve the equation step-by-step: $$120x + 400x - 800 = 6480$$ $$520x - 800 = 6480$$ $$520x = 7280$$ $$x = \frac{7280}{520}$$ $$x = 14$$ Hence, the number of Type $A$ valves sold is **14**.
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