I am not 100% sure if this is the right approach -
A stockbroker has made a profit on 80% of his 40 trades this year.
(80/100) * 40 = 32 profits ; so 8 losses (total 40 trades)
The maximum number of consecutive trades that the stockbroker can lose before his profitable trades drop below 50% for the year.
okay now, if he lost 1 more trade the equation becomes
32 profits
9 loss
total trades 41
profit margin = (profit)/total trades = x/100
32/41 = x/100
profit margin deceases to 78.04%
if he lost another consecutive trade the equation becomes
32 profits
10 loss
total trades 42
profit margin = 32/42 = x/100
profit margin decreases to 76.19
Instead of calculating for each and every consecutive loss, we can directly assume he lost 23 consecutive trades (since we are comparing with quantity A which is 23)
If he lost 23 consecutive trades
32 profits
23 loss
total trades 55
profit margin => 32/55 = x/100
x = 58.18 %
So he has to lose more than 23 consecutive trades for his profit to fall below 50%
Quantity (B) greater