Hi pawan,
We will have to consider the total cost price i.e. 6000 and not the cp of 50 toys alone
Net profit or loss is calculated based on total selling price - total cost price

So, CP=6000, 
To make a profit of 1200, total selling price = 7200
Selling price of each toy = 7200/50 = 144
Percentage of 56 in 200 is 28%

This question is from CAT 2017 and I think the language is quite clear.

There are 60 toys initially of which 10 are destroyed. How should the selling price (and discount) be changed to keep the profit constant.

Hi Saikrishna,
Note that the overall cost price will remain the same
i.e. although 10 toys are damaged, Fatima did pay for it....
So essentially, cost price is same, profit is same, therefore, cp+profit=sp is also same
The only factor changing is the unit sp
In first unit cp = 72c/60=1.2c,  In second case, unit sp = 72c/50=1.44c
Hope this clarifies:)

The fact that 10 toys are destroyed will count in the cost.So, when we are calculating the total cost, we need to take the total cost of 60 toys. As the amount of profit is the same, the total selling price of the 60 toys should now be recovered by selling 50 toys.

Hi Nikhil Reddy, 
The fact that 10 toys are destroyed will count in the cost. So, when we are calculating the total cost, we need to take the total cost of 60 toys. As the amount of profit is the same, the total selling price of the 60 toys should now be recovered by selling 50 toys.
Therefore, the new selling price will be 7200/50 = 144 ( Your assumption is wrong, as the cost of 10 toys which are destroyed will also has to be counted in the cost price)
Therefore, the discount percentage is (200-144)/200*100 = 28%
I hope this helps!