A shopkeeper gives 4 items free of cost with every 21 items and a discount of 25% is also offered to the trader and the shopkeeper still gains 55% profit , Find the ratio of MP:CP.

Solution(By Examveda Team)

Let CP of the item = X.
As he gets 55% profit, so,
SP = X + 55% of X = 1.55X
It is given that he incurs loss by selling 25 articles at the cost of 21 articles Loss = (25 - 21)/25 = 16%.
Now, His,
SP = SP - 16% of SP = 0.84*SP
So,
This SP must be equal to actual SP.
0.84SP = 1.55X
SP = 1.55X/0.84 = 1.84X --------------------(1)
This selling price come after allowing 25% discount on MP.
Let MP = Y
SP = Y - 25% of Y
1.84X = 0.75Y
Y/X = 1.84/0.75
Y/X = 63/155
So,
CP : SP = 63 : 155.