Question: Question 13. Gold and silver are mixed in the ratio $3:7$ by weight. If the total mixture weighs $250g$, how much gold is there?
A) $65g$
B) $70g$
C) $75g$
D) $80g$
1. **State the problem:** We have a mixture of gold and silver in the ratio $3:7$ by weight, and the total weight is $250g$. We need to find the weight of gold.
2. **Formula and rules:** If two quantities are in ratio $a:b$, then the total parts are $a+b$. The quantity corresponding to $a$ is given by $$\frac{a}{a+b} \times \text{total}$$
3. **Apply the formula:** Here, gold corresponds to $3$ parts and silver to $7$ parts, so total parts = $3 + 7 = 10$.
4. **Calculate gold weight:**
$$\text{Gold weight} = \frac{3}{10} \times 250 = 75$$
5. **Answer:** The weight of gold in the mixture is $75g$.
**Final answer:** Option C) $75g$