kop wrote:Initially, the men and women in a room were in the ratio of 4 : 5. Then, 2 men
entered the room and 3 women left the room. Then, the number of women doubled.
Now there are 14 men in the room. How many women are currently in the
room?

Please help me with this, can someone explain some easy method to solve these kind of problems?

The tricky part of this information is the order in which the information is presented. This order SUGGESTS that we may need to create a complicated algebraic expression that uses ratios. However, let's focus solely on the information about the MEN.

We had some men in the room. Then 2 men entered. And then...(later in the information), we see that there are now 14 men in the room.

So, INITIALLY, there were 12 men in the room.

We'll now use this information to determine the number of women that were INITIALLY in the room.
We're told: Initially, the men and women in a room were in the ratio of 4 : 5
So, if there were 12 men in the room, then there were 15 women in the room (since the ratio 12 : 15 is equivalent to the ratio 4 : 5)

So, INITIALLY, 15 women were in the room.
3 women left the room... this leaves 12 women in the room.
Then, the number of women doubled.... now there are 24 women in the room.

Answer: 24

Cheers,
Brent