A man buys shares in stock A and stock B on the stock exchange. Stock A cost $10 a share and stock B cost $20 a share. The total value of shares when he purchased them was $2000.The value of stock A rises by 10% and the value of stock B falls by 5%. Now the total value of his shares is $2050.How many shares in stock B does he hold?

Let's denote the number of shares in stock A as "a" and the number of shares in stock B as "b".

From the problem, we know that:

10a + 20b = 2000 (This is because the total value of the shares when he purchased them was $2000)

After the value of stock A rises by 10% and the value of stock B falls by 5%, the total value of his shares is $2050. This gives us another equation:

1.110a + 0.9520b = 2050

Solving these two equations will give us the values of a and b.

First, let's simplify the equations:

a + 2b = 200 (Divide the first equation by 10)

11a + 19b = 205 (Multiply the second equation by 10)

Now, let's multiply the first equation by 11 and the second equation by 1:

11a + 22b = 2200

11a + 19b = 2050

Subtract the second equation from the first:

3b = 150

So, b = 150 / 3 = 50

Therefore, the man holds 50 shares in stock B.

Let's denote the number of shares the man bought in stock A as "a" and the number of shares he bought in stock B as "b".

From the problem, we know that:

10a + 20b = 2000 (This is because the total value of the shares he bought was $2000)

After the value of stock A rises by 10% and the value of stock B falls by 5%, the total value of his shares is $2050. This gives us another equation:

1.1 * 10a + 0.95 * 20b = 2050

Solving these two equations simultaneously will give us the values of a and b.

First, let's simplify the second equation:

11a + 19b = 2050

Now, let's multiply the first equation by 11 and the second equation by 10:

110a + 220b = 22000 110a + 190b = 20500

Subtract the second equation from the first:

30b = 1500

Solving for b gives us b = 50.

So, the man holds 50 shares in stock B.