Anuj purchases two articles P and Q at the same price. Later, Anuj sells both articles P and Q to Raju at the same price of Rs 350 each. His profit percentage on article P was 'a'%, while his profit percentage on article Q was 'b'%, since he calculated his profit percent for article Q on the selling price. If further, Raju sells one of the items to Joy at (a − 9)% profit, then determine the cost price of the item for Joy. (Note: The value of ‘a’ is 25% more than the value of ‘b’.)

ATQ, Let CP of P and Q = ‘c’ Let SP of P and Q = 350 So, profit for Q is on SP For Q = profit of b% is calculated on SP b = [(350 – c)/350] × 100 For P = profit of a% is calculated on CP a = [(350 – c)/c] × 100 In note it is given that a is 25% more than b [(350 – c)/c] × 100 = (125/100) × [(350 – c)/350] × 100 By solving, we get c = 280 Therefore, CP of P = 280 and Q = 280 Now we find the value of ‘b’ b = [(350 – 280)/350] × 100 = 20% a = [(350 – 280)/280] × 100 = 25% Now CP for Raju =350 Now Raju sold product for (a - 9)% profit = 25- 9 =16% profit SP for Raju = 116% of 350 = 406