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# The average age of a woman and her daughter is $25\ yr$. The ratio of their ages is $7: 3$, respectively. What will be the ratio of their ages after $9$ yr?

**Given: **The average age of a woman and her daughter is $25$ year. The ratio of their ages is $7: 3$, respectively.

**To do:** To find the find the ratio of their ages after $9$ yr.

**Solution:**

Let $7x$ and $3x$ be the ages of woman and her daughter respectively.

As, given, the average age of a woman and her daughter is $25$ year

$\Rightarrow \frac{7x+3x}{2}=25$

$\Rightarrow \frac{10x}{2}=25$

$\Rightarrow 10x=50$

$\Rightarrow x=\frac{50}{10}=5$

Therefore, Age of woman$=7x=7\times5=35$ year

Age of daughter$=3x=3\times5=15$ year

**After $9$ yr:-**

Age of woman$=35+9=44$ year

Age of daughter$15+9=24$ year

Ratio between their ages after $9$ years$=\frac{44}{24}=\frac{11}{6}=11:6$

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