A manufacturer reduces the cost of production of an item by 25% but left the S.P unchanged, as a result of which his profit percentage increased by 40 percentage point. What will be his profit percentage if he reduces the cost of production by further 20%?

Hi, Let the original Cost Price be 100. Therefore Selling Price will be 100+ x, where "x" is both the profit and the profit percentage(Since the base is 100).
Since the CP is reduced by 25%. New CP = 75.
Therefore new profit percentage = (100+x-75/75)*100 (S.P will be 100+x)
Therefore new profit percentage = (25+x)(100)/75.
Now it says that this new profit percentage is 40 percentage point higher than the original.
Original profit percentage= x
Therefore (25+x)(100)/75= x+40
Therefore 2500+100x= 75x+ 3000
Therefore x= 20.
Therefore Selling price = 120
Now if we further reduce the production cost by 20 %, new prod cost will be 0.8 * 75= 60
Since CP=60 and SP=120
New profit percentage= 100.