The ratio between male and female members in a club is $2 : 3$. If the number of male members is increased by $200$, the ratio becomes $5 : 6$. How many female members are there in the club?

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**Solution:**

1. Let the number of male members be $2x$ and female members be $3x$ (since the ratio is $2 : 3$).

2. After increasing male members by $200$, the number of male members becomes $2x + 200$.

3. The new ratio is given as $5 : 6$, so:
   $$\frac{2x + 200}{3x} = \frac{5}{6}$$

4. Cross multiply:
   $$6(2x + 200) = 5(3x)$$

5. Expand:
   $$12x + 1200 = 15x$$

6. Rearranging:
   $$15x - 12x = 1200$$
   $$3x = 1200$$
   $$x = 400$$

7. Number of female members = $3x = 3 	imes 400 = 1200$

**Answer:** $1200$

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