The ratio of the number of twenty-cent coins to the number of one-dollar coins in a bag was 5 : 12 at first.Jerry took 10 one-dollar coins from the bag and exchanged them for twenty-cent coins.He then put the twenty-cent coins back into the bag.The ratio of the number of twenty-cent coins to the number of one-dollar coins in a bag became 3 : 2.How many twenty-cent coins were there in the end?

Let's break down the problem step by step:

1. We know that the initial ratio of twenty-cent coins to one-dollar coins was 5:12. Let's represent the number of twenty-cent coins as 5x and the number of one-dollar coins as 12x.

2. Jerry took 10 one-dollar coins from the bag, so the number of one-dollar coins became 12x - 10.

3. He exchanged these 10 one-dollar coins for twenty-cent coins. Since one dollar is equal to five twenty-cent coins, he got 10 * 5 = 50 twenty-cent coins.

4. He put these 50 twenty-cent coins back into the bag, so the number of twenty-cent coins became 5x + 50.

5. Now, the ratio of the number of twenty-cent coins to the number of one-dollar coins in the bag became 3:2. So, we can write the equation as (5x + 50) / (12x - 10) = 3/2.

6. Solving this equation will give us the value of x.

7. Once we have the value of x, we can substitute it back into the equation 5x + 50 to find the number of twenty-cent coins in the end.

Let's solve the equation:

Cross multiply to get rid of the fraction: 2*(5x + 50) = 3*(12x - 10) => 10x + 100 = 36x - 30 => 26x = 130 => x = 5

Substitute x = 5 into the equation 5x + 50: => 5*5 + 50 = 25 + 50 = 75

So, there were 75 twenty-cent coins in the end.